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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 02:02:47 +0000Bianchi type I cosmological models
https://resolver.caltech.edu/CaltechETD:etd-10162002-080822
Authors: {'items': [{'id': 'Jacobs-K-C', 'name': {'family': 'Jacobs', 'given': 'Kenneth Charles'}, 'show_email': 'NO'}]}
Year: 1969
DOI: 10.7907/KSSQ-R708
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
This thesis begins with a brief review of observations of cosmological interest and with a sketch of the "standard" spatially homogeneous and isotropic cosmological models of our Universe that are currently in vogue. Following this introduction we investigate in great detail anisotropic cosmologies and cosmological models of Bianchi Type I. Our primary goal is to understand the consequences of expansion anisotropies in the general relativistic, hot big-bang theory of cosmology.
We use the Einstein field equations with vanishing cosmological constant, and Maxwell's equations, to study the temporal evolution of anisotropic Bianchi Type I cosmologies. These cosmologies are spatially homogeneous, but anisotropic; and they have no rotation. We consider only cosmologies with the "flat", diagonal, Bianchi Type I metric ds[superscript 2] - dt[superscript2] - A[superscript 2](t)dx[superscript 2] - B[superscript 2](t)dy[superscript 2] - C[superscript 2](t)dz[superscript 2].
We begin by studying the general properties of Bianchi Type I cosmologies. Then we consider the stress-energy tensor for massless-particle gases (either degenerate or non-degenerate) which decouple from thermal equilibrium and become freely-propagating in our diagonal Bianchi Type I metric. We investigate the dynamical effects of anisotropic neutrino stresses, and we show how neutrino viscosity damps out most of the existing expansion anisotropies when neutrinos decouple.
Finally, we elucidate the structure and properties of the Einstein field equations for anisotropic Bianchi Type I cosmologies by deriving a large number of analytical and numerical solutions to these equations. Our stress-energy tensor consists, in general, of perfect-fluid matter with the barotropic equation of state p[subscript m] = [gamma] [rho][subscript m] (0 [<=] [gamma] [<=] 1), and a uniform comoving magnetic field, with energy-density [rho][subscript b], aligned along the z-axis. We first consider the PERFECT-FLUID case where [rho][subscript b] = 0. We find the general analytical solution (for all [gamma]), and construct semi-realistic cosmological models of our Universe using this solution. Then we consider the PERFECT-FLUID-MAGNETIC case where [rho][subscript b] [is not equal to] 0. We derive several analytical solutions, find the behavior near the initial physical singularity for the remaining cases, and study those remaining cases by numerical integration of the field equations. We then consider semi-realistic PERFECT-FLUID-MAGNETIC cosmological models of our Universe.
In our semi-realistic cosmological models we study the possible effects of expansion anisotropies and of a uniform primordial magnetic field upon the following: (a) the type of initial physical singularity, (b) the thermal history and temporal evolution of our Universe, (c) primordial element formation, (d) the time when expansion anisotropies become small, and (e) the temperature isotropy of the observed 2.7[degrees]K cosmic microwave radiation.
https://thesis.library.caltech.edu/id/eprint/4107The stability of relativistic, spherically symmetric star clusters
https://resolver.caltech.edu/CaltechETD:etd-10152002-160828
Authors: {'items': [{'id': 'Ipser-J-R', 'name': {'family': 'Ipser', 'given': 'James Reid'}, 'show_email': 'NO'}]}
Year: 1969
DOI: 10.7907/GF6C-JN05
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
It has been suggested that very dense star clusters might play important roles in quasi-stellar sources and in the nuclei of certain galaxies, where violent events occur. Such star clusters should become unstable against relativistic gravitational collapse when, in the course of evolution, they contract down to a certain critical density. In this thesis the study of the relativistic instability which triggers such collapse is initiated: The theory of the stability of a spherically symmetric star cluster against small radial perturbations is developed within the framework of general relativity. Collisions between stars in the cluster are neglected, since in realistic situations the time scale for collisions should be much greater than the time scale for the growth of the relativistic instability. The equation of motion governing the small radial perturbations of a spherical cluster is derived and is shown to be self-conjugate. Associated with the equation of motion is a dynamically conserved quantity, and a multidimensional variational principle for the normal modes of radial pulsation. The variational principle provides a necessary and sufficient criterion for the stability of the cluster. Also derived are much simpler, one-dimensional, sufficient (but not necessary) criteria for stability. The most important sufficient criterion is this: A relativistic, spherical cluster is stable against radial perturbations if the gas sphere with the same distributions of density and pressure is stable against radial perturbations with adiabatic index [Gamma][subscript 1] = ([rho] + p)p[subscript -1](dp/dr) (d[rho]/dr)[superscript -1].
The stability criteria are used to diagnose numerically the stability of (i) clusters of identical stars with heavily-truncated Maxwell-Boltzmann velocity distributions, and (ii) clusters whose densities and isotropic pressures obey polytropic laws of index 2 or 3. The calculations show that a cluster of either type is unstable against collapse if the redshift of a photon emitted from its center and received at infinity is z[subscript c][...] 0.5. The cluster is stable if z[subscript c][...]0.5.
For purposes of motivation, two new theorems on the theory of the stability of highly relativistic stars (not star clusters!) are also presented in this thesis. The first theorem states that a highly relativistic, spherical star is stable if and only if its adiabatic index (assumed to be constant in the interior regions) is greater than a certain critical value, [gamma][subscript crit], which depends in a specified way on the high-density equation of state. Because of relativistic effects this critical value is somewhat larger than the Newtonian value [gamma][subscript crit] = 4/3. The second theorem shows that, at high central densities, the curves of - (binding energy) versus radius for certain hot, isentropic sequences of stellar models must exhibit damped clockwise spirals. This spiraling reflects the onset of instability in one radial mode of pulsation after another as the central density increases along the sequence.
https://thesis.library.caltech.edu/id/eprint/4096The coupling of gravitational radiation to nonrelativistic sources
https://resolver.caltech.edu/CaltechETD:etd-10152002-090530
Authors: {'items': [{'id': 'Burke-W-L', 'name': {'family': 'Burke', 'given': 'William Lionel'}, 'show_email': 'NO'}]}
Year: 1969
DOI: 10.7907/89HA-6J10
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
This thesis examines the problem of the coupling of gravitational radiation to its sources in the limit of weak fields and slowly-moving sources; it shows in detail how the irreversibility caused by the escape of radiation can be included in the formalism.
The usual slow-motion expansions of General Relativity (EIH and post-Newtonian) have the difficulty that they are not uniformly valid for large distances - distances where radiation becomes important and where the outgoing wave-boundary condition must be imposed. This difficulty is eliminated by using the method of matched asymptotic expansions. A second asymptotic expansion, in the same slowness parameter as enters in the near zone, is used to represent the radiation. This outer expansion provides matching conditions on the inner expansion that generate radiative corrections to the inner expansion.
Using this technique we show that the escape of radiation leads to an extraction of energy from the sources, without ever having to define the energy carried in the gravitational waves. The damping is found by calculating the work done by the fields that react back on the source. Explicit expressions are given for these fields, and these can be used to calculate, in lowest order, all the irreversible effects caused by radiation.
In this thesis the problem of calculating radiation reaction for bodies with very weak gravitational fields (U/c[superscript 2] << v[superscript 2]/c[superscript 2] << 1) is solved definitely. The case of gravitationally bound systems (U/c[superscript 2] [...] v[superscript 2/c[superscript 2] << 1) is discussed and a program for dealing with this case is set up, but the calculations for this case have not yet been done.https://thesis.library.caltech.edu/id/eprint/4091Theoretical Frameworks for Testing Relativistic Gravity; The Parametrized Post-Newtonian Formalism
https://resolver.caltech.edu/CaltechETD:etd-09302005-113319
Authors: {'items': [{'id': 'Will-Clifford-Martin', 'name': {'family': 'Will', 'given': 'Clifford Martin'}, 'show_email': 'NO'}]}
Year: 1971
DOI: 10.7907/NQNB-RK02
Increasing sophistication and precision of experimental tests of relativistic gravitation theories has led to the need for a detailed theoretical framework for analysing and interpreting these experiments. Such a framework is the Parametrized Post-Newtonian (PPN) formalism, which treats the post-Newtonian limit of arbitrary metric theories of gravity in terms of nine metric parameters, whose values vary from theory to theory. The theoretical and experimental foundations of the PPN formalism are laid out and discussed, and the detailed definitions and equations for the formalism are given. It is shown that some metric theories of gravity predict that a massive, self-gravitating body's passive gravitational mass should not be equal to its inertial mass, but should be an anisotropic tensor which depends on the body's self-gravitational energy (violation of the "principle of equivalence"). Two theorems are presented which probe the theoretical structure of the PPN formalism. They state that (i) a metric theory of gravity possesses post-Newtonian integral conservation laws if and only if its nine PP parameters have values which satisfy a set of seven constraint equations, and (ii) a metric theory of gravity is invariant under asymptotic Lorentz transformations if and only if its PPN parameters satisfy a set of three constraint equations. Some theories of gravity (including Whitehead's theory and theories which violate one of the "Lorentz-invariance" parameter constraints) are shown to predict an anisotropy in the Newtonian gravitational constant. Gravimeter data on the tides of the solid Earth are used to put an upper limit on the magnitude of the predicted anisotropy, and thence to rule out such theories.https://thesis.library.caltech.edu/id/eprint/3839Nonspherical perturbations of relativistic gravitational collapse
https://resolver.caltech.edu/CaltechTHESIS:01192010-090920179
Authors: {'items': [{'id': 'Price-R-H', 'name': {'family': 'Price', 'given': 'Richard H.'}}]}
Year: 1971
DOI: 10.7907/1EGC-Y160
It is known that there can be no gravitational, electromagnetic, or scalar field perturbations (except angular momentum) of a Schwarzschild black hole. A gravitationally collapsing star with nonspherical perturbations must therefore radiate away its perturbations or halt its collapse. The results of computations in comoving coordinates are presented to show that the scalar field in a collapsing star neither disappears nor halts the collapse, as the star passes inside its gravitational radius.
On the star's surface, near the event horizon, the scalar field varies as a_1 + a_2 exp (-t/2M) due to time dilation. The dynamics of the field outside the star can be analyzed with a simple wave equation containing a spacetime-curvature induced potential. This potential is impenetrable to zero-frequency waves and thus a_1, the final value of the field on the stellar surface, is not manifested in the exterior; the field vanishes. The monopole perturbation falls off as t^(-2); higher ℓ-poles fall off as ℓn t/t^(2ℓ+3).
The analysis of scalar-field perturbations works as well for electromagnetic and gravitational perturbations and also for zero-restmass perturbation fields of arbitrary integer spin. All these perturbation fields obey wave equations with curvature potentials that differ little from one field to another. For all fields, radiatable multipoles (ℓ ≥ spin of the field) fall off as ℓnt/t^(2ℓ+3).
https://thesis.library.caltech.edu/id/eprint/5526Relativistic velocity - potential hydrodynamics and stellar stability
https://resolver.caltech.edu/CaltechTHESIS:03212016-112353716
Authors: {'items': [{'id': 'Schutz-Bernard-Frederick', 'name': {'family': 'Schutz', 'given': 'Bernard Frederick'}}]}
Year: 1972
DOI: 10.7907/05NX-9C06
<p>The equations of relativistic, perfect-fluid hydrodynamics are cast in Eulerian form using six scalar "velocity-potential" fields, each of which has an equation of evolution. These equations determine the motion of the fluid through the equation </p>
<p>U<sub>ʋ</sub>=µ<sup>-1</sup> (ø,<sub>ʋ</sub> + αβ,<sub>ʋ</sub> + ƟS,<sub>ʋ</sub>).</p>
<p>Einstein's equations and the velocity-potential hydrodynamical equations
follow from a variational principle whose action is</p>
<p>I = (R + 16π p) (-g)<sup>1/2</sup> d<sup>4</sup>x,</p>
<p>where R is the scalar curvature of spacetime and p is the pressure of the fluid. These equations are also cast into Hamiltonian form, with Hamiltonian density –T<sub>0</sub><sup>0</sup> (-g<sup>oo</sup>)<sup>-1/2</sup>.</p>
<p>The second variation of the action is used as the Lagrangian governing the evolution of small perturbations of differentially rotating stellar models. In Newtonian gravity this leads to linear dynamical stability criteria already known. In general relativity it leads to a new sufficient condition for the stability of such models against arbitrary perturbations.</p>
<p>By introducing three scalar fields defined by</p>
<p>ρ ᵴ = <u>∇</u>λ + <u>∇</u>x(x<u>i</u> + <u>∇</u>xɣ<u>i</u>)</p>
<p>(where ᵴ is the vector displacement of the perturbed fluid element, ρ is the mass-density, and <u>i</u>, is an arbitrary vector), the Newtonian stability criteria are greatly simplified for the purpose of practical applications. The relativistic stability criterion is not yet in a form that permits practical calculations, but ways to place it in such a form are discussed.</p>
https://thesis.library.caltech.edu/id/eprint/9630Applications of black-hole perturbation techniques
https://resolver.caltech.edu/CaltechETD:etd-08252008-111253
Authors: {'items': [{'id': 'Press-W-H', 'name': {'family': 'Press', 'given': 'William H.'}, 'show_email': 'NO'}]}
Year: 1973
DOI: 10.7907/0HKZ-DJ23
Separable, decoupled differential equations which describe gravitational, electromagnetic, and scalar perturbations of nonrotating (Schwarzschild) and rotating (Kerr) black holes have recently become available. Fortuitously, many interesting astrophysical processes near black holes can accurately be studied with these perturbation equations. A number of such processes are here investigated (as well as some matters of principle in pure relativity): "vibrations" of black holes, and the long wave-trains of gravitational waves which such vibrations may generate; the spectrum and intensity of gravitational radiation from a particle falling radially into a Schwarzschild hole; the physical significance of the Newman-Penrose conserved quantities, the result that they are never physically measurable and do not always exist; the time evolution of a rotating black hole immersed in a static scalar field, a quantitative calculation of the hole's "spin-down" and "alignment"; scalar-field calculations of superradiant wave scattering from a rotating black hole, and of the possibility of "floating orbits" — these are both wave processes which extract a hole's rotational energy. Included is a discussion of how these scalar-field results can be extended to the electromagnetic and gravitational cases. The most important perturbation problem yet to be solved is the question of whether rotating black holes are stable (against processes which would spontaneously emit gravitational waves). The astrophysical implications of instabilities are discussed, and a method for deciding the stability question (on which work is in progress) is outlined in detail. An appendix includes additional work on peripherally related matters. Several papers included in this thesis are extended from their published form by a more detailed discussion of numerical methods.
https://thesis.library.caltech.edu/id/eprint/3221Metric Theories of Gravity and their Astrophysical Implications
https://resolver.caltech.edu/CaltechTHESIS:08282017-154628547
Authors: {'items': [{'id': 'Ni-Wei-Tou', 'name': {'family': 'Ni', 'given': 'Wei-Tou'}}]}
Year: 1973
DOI: 10.7907/MCQM-3M81
<p>The increasing importance of relativistic gravity in astrophysics has led to the need for a detailed analysis of theories of gravity and their viability. Accordingly, in this thesis, metric theories of gravity are compiled, and are classified into four groups: (i) general relativity
(ii) scalar-tensor theories (iii) conformally flat theories and (iv) stratified theories. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained. These results, when combined with experimental data and with recent work by Nordtvedt and Will, show that, of all theories thus far examined by our group, the only currently viable ones are (i) general relativity, (ii) the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan, (iii) recent, (as yet unpublished ) vector-tensor theory by Nordtvedt, Hellings,
and Will, and (iv) a new stratified theory by the author, which is presented for the first time in this thesis.</p>
<p>The PPN formalism is used to analyze stellar stability in any metric theory of gravity. This analysis enables one to infer, for any given gravitation theory, the extent to which post-Newtonian effects induce instabilities in white dwarfs, in neutron stars, and in supermassive stars. It also reveals the extent to which our current empirical knowledge of post-Newtonian gravity (based on solar-system experiments) actually guarantees that relativistic instabilities exist. In particular, it shows that for "conservative theories of gravity", current solar-system experiments guarantee that relativistic corrections do induce
dynamical instabilities in stars with adiabatic indices slightly greater than 4/3, while for "non-conservative theories", current experiments do not permit any firm conclusion.
</p>https://thesis.library.caltech.edu/id/eprint/10395Conserved quantities and the formation of black holes in the Brans-Dicke theory of gravitation
https://resolver.caltech.edu/CaltechTHESIS:06022015-082916942
Authors: {'items': [{'id': 'Dykla-J-J', 'name': {'family': 'Dykla', 'given': 'John Joseph'}, 'show_email': 'NO'}]}
Year: 1973
DOI: 10.7907/h455-hg42
<p>In Part I, we construct a symmetric stress-energy-momentum
pseudo-tensor for the gravitational fields of Brans-Dicke theory, and use this to establish rigorously conserved integral expressions for energy-momentum P<sup>i</sup> and angular momentum J<sup>ik</sup>. Application of the two-dimensional surface integrals to the exact static spherical vacuum solution of Brans leads to an identification of our conserved mass with the active gravitational mass. Application to the distant fields of an arbitrary stationary source reveals that P<sup>i</sup> and J<sup>ik</sup> have the same physical interpretation as in general relativity. For gravitational waves whose wavelength is small on the scale of the background radius of curvature, averaging over several wavelengths in the Brill-Hartle-Isaacson manner produces a stress-energy-momentum tensor for gravitational radiation which may be used to calculate the changes in P<sup>i</sup> and J<sup>ik</sup> of their source. </p>
<p>In Part II, we develop strong evidence in favor of a conjecture by Penrose--that, in the Brans-Dicke theory, relativistic gravitational collapse in three dimensions produce black holes identical to those of general relativity. After pointing out that any black hole solution of general relativity also satisfies Brans-Dicke theory, we establish the Schwarzschild and Kerr geometries as the only possible spherical and axially symmetric black hole exteriors, respectively. Also, we show that a Schwarzschild geometry is necessarily formed in the collapse of an uncharged sphere.</p>
<p>Appendices discuss relationships among relativistic gravity theories and an example of a theory in which black holes do not exist.</p>
https://thesis.library.caltech.edu/id/eprint/8966Frameworks for analyzing and testing theories of gravity
https://resolver.caltech.edu/CaltechETD:etd-04092004-111803
Authors: {'items': [{'id': 'Lee-David-Li', 'name': {'family': 'Lee', 'given': 'David Li'}, 'show_email': 'NO'}]}
Year: 1974
DOI: 10.7907/KC8C-MS78
This thesis presents theoretical frameworks for the analysis and testing of gravitation theories - both metric and non-metric. For non-metric theories, the high-precision Eotvos-Dicke-Braginskii (EDB) experiments are demonstrated to be powerful tests of their gravitational coupling to electromagnetic interactions. All known non-metric theories are ruled out to within the precision of the EDB experiments. We present a new metric theory of gravity that cannot be distinguished from general relativity in all current and planned solar system experiments. However, this theory has very different gravitational-wave properties. Hence, we point out the need for further tests of metric theories beyond the Parametrized Post-Newtonian formalism, and emphasize the importance of the observation of gravitational waves as a tool for testing relativistic gravity in the future. A theory-independent formalism delineating the properties of weak, plane gravitational waves in metric theories is set up.
General conservation laws that follow from variational principles in metric theories of gravity are investigated.https://thesis.library.caltech.edu/id/eprint/1317Perturbations of a Rotating Black Hole
https://resolver.caltech.edu/CaltechETD:etd-08022006-094950
Authors: {'items': [{'id': 'Teukolsky-Saul-Arno', 'name': {'family': 'Teukolsky', 'given': 'Saul Arno'}, 'orcid': '0000-0001-9765-4526', 'show_email': 'NO'}]}
Year: 1974
DOI: 10.7907/N3AW-PV92
Decoupled, separable equations describing perturbations of a Kerr black hole are derived. These equations can be used to study black-hole processes involving scalar, electromagnetic, neutrino or gravitational fields. A number of astrophysical applications are made: Misner's idea that gravitational synchrotron radiation might explain Weber's observations is shown to be untenable; rotating black holes are shown to be stable against small perturbations; energy amplification by "superradiant scattering" of waves off a rotating black hole is computed; the "spin down" (loss of angular momentum) of a rotating black hole caused by a stationary non-axisymmetric perturbation is calculated.https://thesis.library.caltech.edu/id/eprint/2997Time-dependent accretion disks around compact objects. Theoretical frameworks for analyzing and testing gravitation theories
https://resolver.caltech.edu/CaltechETD:etd-11112003-091837
Authors: {'items': [{'id': 'Lightman-A-P', 'name': {'family': 'Lightman', 'given': 'Alan Paige'}, 'show_email': 'NO'}]}
Year: 1974
DOI: 10.7907/1QYN-CQ82
Part I.
The theory of time-independent accretion disks around compact objects is developed, generalizing the stationary models of various authors to allow time dependence on the radial-flow time scale. Equations are derived for the time evolution of matter surface density [Sigma] and for implicit expressions of relevant disk variables in terms of [Sigma]. Analytic and numerical studies of these equations yield numerical models of mass accretion from a disk onto a compact object and a discovery of the unstable nature of the "inner region" of the disk, causing a breakdown of current accretion disk models.
Part II.
Theoretical frameworks for analyzing and testing gravitation theories are developed for both nonmetric and metric theories. Highly precise experimental confirmation of the Weak Equivalence Principle is shown to be deadly if not fatal evidence for ruling out all nonmetric theories of gravity. For the class of metric theories we demonstrate the necessity for going beyond current frameworks of analysis (e.g.,the PPN framework) by constructing a new theory of gravity identical to GRT in the Post-Newtonian limit. As a first step in transcending current frameworks, we develop a formalism for delineating and testing all metric theories of gravity on the basis of their gravitational-wave properties and thereby emphasize gravitational-wave observations as a future tool for testing gravitation theories. We also investigate conservation laws and some common properties of Lagrangian-based metric theories of gravity.https://thesis.library.caltech.edu/id/eprint/4501Accretion into and emission from black holes
https://resolver.caltech.edu/CaltechTHESIS:07192012-091529776
Authors: {'items': [{'id': 'Page-D-N', 'name': {'family': 'Page', 'given': 'Don Nelson'}, 'show_email': 'NO'}]}
Year: 1976
DOI: 10.7907/RAEC-8822
<p>Analyses are given of various processes involving matter falling
into or coming out of black holes.</p>
<p>A significant amount of matter may fall into a black hole in a
galactic nucleus or in a binary system. There gas with relatively high
angular momentum is expected to form an accretion disk flowing into the
hole. In this thesis the conservation laws of rest mass, energy, and
angular momentum are used to calculate the radial structure of such a
disk. The averaged torque in the disk and flux of radiation from the
disk are expressed as explicit, algebraic functions of radius.</p>
<p>Matter may be created and come out of the gravitational field of
a black hole in a quantum-mechanical process recently discovered by
Hawking. In this thesis the emission rates of massless particles by
Hawking's process are computed numerically. The resulting power spectra
of neutrinos, photons, and gravitons emitted by a nonrotating hole are
given. For rotating holes, the rates of emission of energy and angular
momentum are calculated for various values of the rotation parameter.
The evolution of a rotating hole is followed as energy and angular
momentum are given up to the emitted particles. It is found that angular
momentum is lost considerably faster than energy, so that a black
hole spins down to a nearly nonrotating configuration before it loses a
large fraction of its mass. The implications are discussed for the lifetimes and possible present configurations of primordial black
holes (the only holes small enough for the emission to be significant
within the present age of the universe.</p>
<p>As an astrophysical application, a calculation is given of the
gamma-ray spectrum today from the emission by an assumed distribution
of primordial black holes during the history of the universe. Comparison
with the observed isotropic gamma-ray flux above about 100 MeV yields
an upper limit of approximately 10^4 pc^(-3) for the average number density
of holes around 5 x 10^(14)g. (This is the initial mass of a nonrotating
black hole that would just decay away in the age of the universe.) The
prospects are discussed for observing the final, explosive decay of an
individual primordial black hole. Such an observation could test the
combined predictions of general relativity and quantum mechanics and
also could provide information about inhomogeneities in the early universe
and about the nature of strong interactions at high temperatures.</p>
https://thesis.library.caltech.edu/id/eprint/7179The Generation of Gravitational Waves
https://resolver.caltech.edu/CaltechTHESIS:08252017-093756825
Authors: {'items': [{'id': 'Kovács-Sándor-János-Jr.', 'name': {'family': 'Kovács', 'given': 'Sándor János, Jr.'}}]}
Year: 1977
DOI: 10.7907/VHQW-W277
<p>This dissertation is written in three tracks. Track 1, (Pages ii-vi)
is intended for those many many people who don't know any physics but who
do know how to read English and a bit of Hungarian perhaps.</p>
<p>Track 2 is intended for those one hundred or so people in the whole
world who do know classical physics and have serious interests in, or
are experts in relativity theory. Papers 1, 2 and 3 dealing with
relativity are entirely Track 2.</p>
<p>The remaining paper is Track 3 and is for the benefit of even fewer
people who have a simultaneous interest in relativity and quantum field
theory.</p>
<p>I will not discuss the abstracts of the individual papers here -
since each paper is preceded by its own abstract. Suffice it to say that this
dissertation is a collection of papers dealing with the theoretical
aspects of how gravitational waves may (or may not) be generated
by gravitational bremsstrahlung, and in Paper 4 Walter and I try to
show that some classical relativity problems may be solved with much
greater ease via a quantum approach.</p>https://thesis.library.caltech.edu/id/eprint/10390Electromagnetic Wave Generation and Propagation in Gravitational Fields
https://resolver.caltech.edu/CaltechTHESIS:08312017-150019175
Authors: {'items': [{'id': 'De-Logi-Walter-K', 'name': {'family': 'De Logi', 'given': 'Walter K.'}}]}
Year: 1978
DOI: 10.7907/es3k-qv56
<p>We use Feynman perturbation techniques to analyze some aspects
of electromagnetic wave generation and propagation in weak gravitational
fields.</p>
<p>In the first part of this report we calculate differential
cross sections dσ/dΩ for the scattering of plane electromagnetic
waves by weakly gravitating and rotating bodies in the long-wavelength
limit (wavelength of incident radiation >> radius of scatterer >> mass
of scatterer). We find that the polarization of right (or left)
circularly polarized electromagnetic waves is unaffected by the
scattering process (i.e., helicity is conserved), and that the two
helicity states of the photon are scattered differently by a rotating
body. This coupling between the photon helicity and the angular
momentum of the scatterer also leads to a partial polarization of
unpolarized incident light.</p>
<p>For the sake of comparison, we also compute the differential
cross sections for the gravitational scattering of scalar and gravitational
waves. For the latter there is neither helicity conservation
nor helicity-dependent scattering; and the angular momentum has no
polarizing effect on incident, unpolarized gravitational waves.</p>
<p>In the second part of this report, we analyze the conversion
of gravitational waves into electromagnetic waves (and vice versa)
under the "catalytic" action of a static electromagnetic background
field. Closed-form differential cross sections are presented for
conversion in the Coulomb field of a point charge, electric and
magnetic dipole fields, and uniform electrostatic and magnetostatic
fields. Using the model calculation of conversion in a Coulomb field,
we discuss the problems that we must face when calculating non-gauge-invariant
transition amplitudes, as is frequently done in the literature.</p>
<p>We conclude this report by pointing out how charged-particle
beams may be used (in principle) as direction-sensitive gravitational-wave detectors.</p>
https://thesis.library.caltech.edu/id/eprint/10406Theoretical investigations of experimental gravitation
https://resolver.caltech.edu/CaltechTHESIS:03152016-161054898
Authors: {'items': [{'email': 'ccaves@unm.edu', 'id': 'Caves-Carlton-Morris', 'name': {'family': 'Caves', 'given': 'Carlton Morris'}, 'show_email': 'YES'}]}
Year: 1979
DOI: 10.7907/H3T8-FQ06
<p>This thesis has two basic themes: the investigation of new experiments
which can be used to test relativistic gravity, and the investigation of new
technologies and new experimental techniques which can be applied to make
gravitational wave astronomy a reality.</p>
<p>Advancing technology will soon make possible a new class of gravitation
experiments: pure laboratory experiments with laboratory sources of non-Newtonian
gravity and laboratory detectors. The key advance in techno1ogy
is the development of resonant sensing systems with very low levels of dissipation.
Chapter 1 considers three such systems (torque balances, dielectric
monocrystals, and superconducting microwave resonators), and it proposes
eight laboratory experiments which use these systems as detectors. For each
experiment it describes the dominant sources of noise and the technology
required.</p>
<p>The coupled electro-mechanical system consisting of a microwave cavity
and its walls can serve as a gravitational radiation detector. A gravitational
wave interacts with the walls, and the resulting motion induces
transitions from a highly excited cavity mode to a nearly unexcited mode.
Chapter 2 describes briefly a formalism for analyzing such a detector, and
it proposes a particular design.</p>
<p>The monitoring of a quantum mechanical harmonic oscillator on which a
classical force acts is important in a variety of high-precision experiments,
such as the attempt to detect gravitational radiation. Chapter 3 reviews
the standard techniques for monitoring the oscillator; and it introduces a
new technique which, in principle, can determine the details of the force
with arbitrary accuracy, despite the quantum properties of the oscillator.</p>
<p>The standard method for monitoring the oscillator is the "amplitude-
and-phase" method (position or momentum transducer with output fed through
a linear amplifier). The accuracy obtainable by this method is limited by
the uncertainty principle. To do better requires a measurement of the type
which Braginsky has called "quantum nondemolition." A well-known quantum
nondemolition technique is "quantum counting," which can detect an arbitrarily
weak force, but which cannot provide good accuracy in determining
its precise time-dependence. Chapter 3 considers extensively a new type
of quantum nondemolition measurement - a "back-action-evading" measurement
of the real part X<sub>1</sub> (or the imaginary part X<sub>2</sub>) of the oscillator's complex
amplitude. In principle X<sub>1</sub> can be measured arbitrarily quickly and arbitrarily
accurately, and a sequence of such measurements can lead to an
arbitrarily accurate monitoring of the classical force.</p>
<p>Chapter 3 describes explicit gedanken experiments which demonstrate that
X<sub>1</sub> can be measured arbitrarily quickly and arbitrarily accurately, it considers
approximate back-action-evading measurements, and it develops a theory
of quantum nondemolition measurement for arbitrary quantum mechanical systems.</p>
<p>In Rosen's "bimetric" theory of gravity the (local) speed of gravitational
radiation v<sub>g</sub> is determined by the combined effects of cosmological
boundary values and nearby concentrations of matter. It is possible for v<sub>g</sub>
to be less than the speed of light. Chapter 4 shows that emission of gravitational
radiation prevents particles of nonzero rest mass from exceeding the
speed of gravitational radiation. Observations of relativistic particles
place limits on v<sub>g</sub> and the cosmological boundary values today, and observations
of synchrotron radiation from compact radio sources place limits on
the cosmological boundary values in the past.</p>https://thesis.library.caltech.edu/id/eprint/9621Studies on Gravitational Waves and Stars with Neutron Cores
https://resolver.caltech.edu/CaltechTHESIS:02172017-144352834
Authors: {'items': [{'id': 'Zimmermann-Mark-Edward', 'name': {'family': 'Zimmermann', 'given': 'Mark Edward'}}]}
Year: 1980
DOI: 10.7907/n4hc-5489
<p>This thesis reports on investigations in two major areas: astrophysics
and relativity. It is divided into six independent chapters.</p>
<p>Chapter I contains estimates of the astrophysically-likely amplitude
of gravitational radiation emitted by the Crab and Vela pulsars. For
my analysis, I model the pulsars as rapidly-rotating, freely-precessing,
rigid or elastic solid bodies. I find that the Crab is likely to produce
gravitational waves at Earth with dimensionless amplitude 10<sup>-27±2</sup>, and
that Vela is likely to give waves one or two orders of magnitude larger.</p>
<p>Chapters II and III study the gravitational radiation produced by
an idealized rotating and freely-precessing rigid body in the weak-field,
slow-motion, small-stresses, quadrupole-moment formalism. Chapter II gives
the results for axisymmetric objects and for arbitrarily shaped objects
undergoing small-angle precession. In that chapter, I also discuss the
application of my results to neutron stars in nature, and I describe in
detail how to analyze the incoming waves and extract information about
their source. Chapter III extends the analysis of Chapter II to the
general case of an arbitrary rigid body undergoing large-angle precession.</p>
<p>Chapter IV considers all astrophysically-reasonable sources of
gravitational waves. Based on a minimal set of "cherished beliefs" about
the universe and about gravitation, I give general upper limits to the
expected intensity of gravitational radiation at the earth, at various
frequencies and from a variety of sources.</p>
<p>Chapter V examines a "natural" coordinate system which might be set
up by a rotating and accelerating observer. I expand the metric through
second-order terms in distance from the origin of the coordinates; from
the metric, I derive the equations of motion for test particles. I
identify many forces and pseudoforces in the equations of motion, and
I discuss how my results may be used to analyze some laboratory gravitational
experiments.</p>
<p>Chapter VI of this thesis is a report on my results in studying nucleo-synthesis
in stars with neutron-star cores. I was not able to generate
any self-consistent models with a total mass of 16 M<sub>⊙</sub>, core mass of 1 M<sub>⊙</sub>,
and core radius of 10 km; nuclear reactions fell short of producing the
needed luminosity by a factor of 25 or more. I describe in detail my
modeling procedures and the reasons for the failure of nucleosynthesis,
and I point out extensions and modifications of my models which may be
more successful.</p>
https://thesis.library.caltech.edu/id/eprint/10058Stationary Spherical Optically Thick Accretion into Black Holes
https://resolver.caltech.edu/CaltechTHESIS:08252017-133002176
Authors: {'items': [{'id': 'Flammang-Richard-Alan', 'name': {'family': 'Flammang', 'given': 'Richard Alan'}, 'show_email': 'NO'}]}
Year: 1982
DOI: 10.7907/t73p-2e81
<p>As its title indicates, this thesis treats the problem of stationary, spherical, optically thick accretion into black holes. By the phrase "optically thick" it is meant that (1) radiative energy transport can be adequately described by the diffusion approximation and (2) the photons are everywhere in local energy equilibrium (LTE) with the accreting gas particles.</p>
<p>In Chapter 1, a general set of equations governing time-independent spherical accretion into black holes is formulated. The equations are fully general relativistic and are applicable to optically thick regions, optically thin regions, and the transition regions which join them. The radiation is treated using frequency-integrated moments. The full, infinite series of moment equations is given, together with the limiting forms the equations take in the optically thick regime.</p>
<p>In Chapter 2, we present the mathematical theory of stationary spherical optically thick accretion. We analyze the integral curves of the differential equations describing the problem. We find a one-parameter family of critical points, where the inflow velocity equals the isothermal sound speed. Physical solutions must pass through one of these critical points. We obtain a complete set of boundary conditions which the solution must satisfy at the horizon of the black hole, and show that these, plus the requirement that the solution pass through a critical point, determine a unique solution to the problem. This analysis leads to a generalization of the well-known Bondi critical point constraint, which arises in the adiabatic accretion problem and which is effective at the point where the inflow velocity equals the adiabatic sound speed. We show that this point can be regarded as a "diffused critical point" in our problem. The analysis also yields a simple expression for the diffusive luminosity at radial infinity. Finally, we find a satisfying explanation for the rather peculiar critical point structure of this problem in an analysis of the characteristics and subcharacteristics present in the problem and in a "hierarchical" analysis of the waves which propagate along them.</p>
<p>In Chapter 3, we apply the theory of optically thick accretion developed in Chapter 2 to a wide range of physically different accretion regimes. Numerical solutions are presented and their physical properties are discussed. For solutions in which radiation pressure P<sub>R</sub> dominates gas pressure P<sub>G</sub>, but in which gas energy density (including its rest-mass) ρ<sub>G</sub> dominates radiation energy density ρ<sub>R</sub>, we pay particular attention to the adabaticity of the flow. Our quantitative results in this regime agree very well with Begelman's (1978) theory. We find the dimensionless number which governs the importance of heat diffusion in our problem and show that it reduces to the idea of "trapping of photons" and to the Péclet number in the appropriate limits. We find that solutions with P<sub>R</sub> > P<sub>G</sub> and ρ<sub>R</sub> > ρ<sub>G</sub> are always essentially adiabatic, owing in part to a relativistic suppression of heat flux which becomes important in this regime. The diffusive luminosity at infinity for these solutions is the Eddington limit of the black hole; with the adiabatic accretion rate, "efficiencies" of up to order unity are possible. We give preliminary consideration to the question of the stability of our solutions against convection and conclude that the Schwarzschild criterion is applicable, even for our non-static accretion flows. We show that solutions with P<sub>R</sub> > P<sub>G</sub> are everywhere stable against convection. On the other hand, solutions which start out at radial infinity with P<sub>G</sub> > P<sub>R</sub> are unstable to convection (if the adiabatic index of the gas γ<sub>G</sub> exceeds 17/12) from radial infinity down to the point where P<sub>R</sub> ~ P<sub>G</sub> and the radiation-gas mixture has attained an adiabatic index of 17/12. The diffusive luminosity at infinity for these solutions is reduced from the Eddington limit of the black hole by the factor (γ<sub>G</sub> - 1)4P<sub>R∞</sub>/γ<sub>G</sub>P<sub>G∞</sub>; it is further reduced by the ratio of the electron scattering opacity to the actual opacity at infinity, if this differs from unity. In most cases, energy diffusion has a negligible effect on the accretion rate of these solutions.</p>https://thesis.library.caltech.edu/id/eprint/10391Stability of Spherically Symmetric, Charged Black Holes and Multipole Moments for Stationary Systems
https://resolver.caltech.edu/CaltechETD:etd-03132009-081222
Authors: {'items': [{'id': 'Gürsel-Halis-Yekta', 'name': {'family': 'Gürsel', 'given': 'Halis Yekta'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/e9t6-dr05
<p>This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.</p>
https://thesis.library.caltech.edu/id/eprint/945Topics in Black-Hole Physics: Geometric Constraints on Noncollapsing, Gravitating Systems and Tidal Distortions of a Schwarzschild Black Hole
https://resolver.caltech.edu/CaltechTHESIS:08232017-105535039
Authors: {'items': [{'id': 'Redmount-Ian-H', 'name': {'family': 'Redmount', 'given': 'Ian H.'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/mp3n-4r06
<p>This dissertation consists of two studies on the general-relativistic theory of black holes. The first work concerns the fundamental issue of black-hole formation: in it I seek geometric constraints on gravitating matter systems, in the special case of axial symmetry, which determine whether or not those systems undergo gravitational collapse to form black holes. The second project deals with mechanical behavior of a black hole: specifically, I study the tidal deformation of a static black hole by the gravitational fields of external bodies.</p>
<p>In the first paper I approach the problem of geometric constraints determining gravitational collapse or non-collapse through the initial-value formalism of general relativity. I construct initial-value data representing noncollapsing, nonsingular, axisymmetric matter systems and examine the constraints imposed on this construction by the initial-value equation derived from the Einstein field equations. The construction consists of a nonsingular, momentarily static interior geometry with nonnegative mass-energy density, matched smoothly to a static, vacuum exterior geometry (described by a Weyl solution of the Einstein field equations) at a boundary surface. The initial-value equation is found to impose restrictions on the choice of the boundary surface for such a system. Two such constraints are obtained here, appropriate to spherical and toroidal interior-region topologies. These constraints are studied by applying them to simple examples of Weyl exterior geometries. The "hoop conjecture" for the general geometric-constraints problem states that a system must collapse to a black hole unless its circumference in some direction exceeds a lower bound of the order of the system's mass. The examples examined here show, however, that the constraints derived in this study are not generally correlated with any simple measure of system size, and thus that they do not embody the hoop conjecture.</p>
<p>The second paper examines the tidal distortion of a Schwarzschild black hole by bodies ("moons") suspended above the horizon on "ropes." A solution of the Einstein field equations is constructed describing this configuration, using the Weyl formalism for axisymmetric, static, vacuum geometries. The intrinsic geometry of the tidally deformed black-hole horizon is obtained from this solution; I construct embedding diagrams to represent the shape of the horizon and the tidal bulges raised on it for both weak and strong perturbations. The relations among the masses of the hole and moons, the binding energy of the system, and the rope density and tension are calculated from the solution and shown to be mutually consistent. Also, the Riemann curvature tensor representing the tidal fields near the horizon is calculated. This solution is found to agree with a previous calculation by Hartle of black-hole tides, in the limit of perturbing moons far from the horizon. In the opposite case of moons very near the horizon, this solution approaches the static limit of the distorted horizon in Rindler space calculated by Suen and Price. The results of this study thus support the use of the Rindler approximation to Schwarzschild spacetime in calculating static black-hole tides, and its extension to dynamical situations.</p>https://thesis.library.caltech.edu/id/eprint/10385Black-Hole Electrodynamics
https://resolver.caltech.edu/CaltechTHESIS:09012017-133647841
Authors: {'items': [{'id': 'Macdonald-Douglas-Alan', 'name': {'family': 'Macdonald', 'given': 'Douglas Alan'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/vv78-at49
<p>This dissertation considers several aspects of the structure and dynamics of electromagnetic fields around black holes. The four-dimensional, covariant laws of electrodynamics are reformulated in a 3 + 1 (space+time) language in which the key quantities are three-dimensional vectors lying in hypersurfaces of a constant global time <i>t</i>. This formulation is applied to the Blandford-Znajek model of power generation in quasars, which consists of a supermassive black hole surrounded by an accretion disk that holds a magnetic field on the hole, with the rotational energy and angular momentum of the hole and disk being extracted by electromagnetic torques. The 3 + 1 formalism allows the theory of stationary, axisymmetric black holes and their magnetospheres to be couched in an "absolute-space/universal-time" language very similar to the flat spacetime theory of pulsar electrodynamics; and this similarity allows fiat-space pulsar concepts to be extended to curved-space black holes. The Blandford-Znajek quasar model is reformulated in terms of a DC circuit-theory analysis, and action principles describing the overall structure of the magnetosphere and the field distribution on the horizon are developed. A general prescription for constructing global models of force-free magnetospheres is developed and this prescription is used to generate numerical models of black-hole magnetospheres for a variety of field configurations and black-hole angular velocities. The electromagnetic boundary conditions at the horizon of a black hole are described in terms of a recently developed "membrane viewpoint". The necessity and efficacy of using a "stretched horizon" in the membrane viewpoint is discussed, and is illustrated by two simple dynamical problems involving electromagnetic fields near black-hole horizons.</p>https://thesis.library.caltech.edu/id/eprint/10410Dynamical Electromagnetic Fields Near Black Holes and Multipole Moments of Stationary, General Relativistic Systems
https://resolver.caltech.edu/CaltechTHESIS:09012017-090944275
Authors: {'items': [{'id': 'Suen-Wai-Mo', 'name': {'family': 'Suen', 'given': 'Wai Mo'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/xayq-7806
<p>This dissertation contains two works; one of the behavior of dynamical electromagnetic fields in the stationary spacetime generated by a black hole, and the other on the structure of a general stationary vacuum spacetime itself.</p>
<p>The study of electromagnetic field is carried out in terms of the "membrane formalism" for black holes; and it is part of a series of papers with the aim of developing that formalism into a complete, self-consistent description of electromagnetic and gravitational fields in a black hole background. Various model problems are presented as aids in understanding the interactions of electromagnetic fields with a black hole, and special attention is paid to the concept of the "stretched horizon" which is vital for the membrane formalism.</p>
<p>The second work develops a multipole moment formalism for a general stationary system in general relativity. The multipole moments are defined in terms of a general formal series solution of the stationary Einstein equation, in analogy to multipole moments in the Newtonian theory of gravity. These relativistic moments exhibit many desirable properties and are shown to be useful in studying the interactions between a gravitating body and an external gravitational field. A model calculation applying the formalism to a black hole interacting with an external multipole field shows that the interaction can be understood in terms of "elastic moduli" of the black-hole horizon.</p>https://thesis.library.caltech.edu/id/eprint/10408Theoretical Investigations in Nonlinear Quantum Optics, Theory of Measurement, and Pulsations of General Relativistic Models of Neutron Stars
https://resolver.caltech.edu/CaltechTHESIS:09062017-132307035
Authors: {'items': [{'id': 'Schumaker-Bonny-Laura', 'name': {'family': 'Schumaker', 'given': 'Bonny Laura'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/fwvz-7t26
<p>This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and moment um variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the ouput modes arise from two-photon transitions, i.e., are created or destroyed two at a time. The states produced by such devices are single-mode and two-mode "squeezed states", special kinds of GPS whose low-noise properties make them attractive for applications in such fields as optical communications and gravitational wave detection. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed as an improved signal-to-noise ratio relative to that obtained with coherent states (the states produced, e.g., by a laser).</p>
<p>The fifth and sixth papers deal with problems of a different nature from that of the previous papers. The fifth paper considers the validity of the "standard quantum limit" (SQL) for measurements which monitor the position of a free mass. It shows specifically that when the pre-measurement wave functions of the free mass and the measuring apparatus(es) are Gaussian (in the general sense, which includes so-called "contractive states"), measurements described by linear couplings to the position or to both the position and momentum are limited by the SQL. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models, and of the gravitational waves they emit.</p>https://thesis.library.caltech.edu/id/eprint/10414Relativistic Stellar Pulsations
https://resolver.caltech.edu/CaltechETD:etd-08262008-093129
Authors: {'items': [{'email': 'lsfinn@psu.edu', 'id': 'Finn-Lee-Samuel', 'name': {'family': 'Finn', 'given': 'Lee Samuel'}, 'show_email': 'YES'}]}
Year: 1987
DOI: 10.7907/T7VS-8648
<p>This thesis consists of studies on the topic of relativistic stellar pulsations.</p>
<p><i>i)</i> A new formalism for the numerical study of <i>g</i>-modes in neutron stars is developed. This formalism avoids pitfalls associated with previous formalisms when applied to the study of these low-frequency modes. The formalism involves a new choice of perturbation variables, the introduction of an "instantaneous gravity" approximation to the field outside the star, and an energy principle for determining gravitational radiation damping times. The formalism is used to study <i>g</i>-modes that arise because of chemical inhomogeneities in neutron star crusts. <i>g</i>-mode frequencies associated with chemical inhomogeneities are found to be much higher than those associated with finite temperature.</p>
<p><i>ii)</i> The relativistic Cowling approximation, introduced by McDermott, Van Horn, and Scholl (1983) and analogous to the Newtonian Cowling approximation, is refined to make it more accurate in the regime of highly relativistic stars. The approximation is used to prove a host of useful theorems regarding the non-radial modes of relativistic stars.</p>
<p><i>iii)</i> Realistic neutron stars have a solid crust, and this will seriously affect their <i>g</i>-modes. The first steps toward developing a theory of non-radial relativistic pulsations in stars with a solid crust is reported on here: the calculation of the shear strain and stress during a pulsation, the introduction of the shear stress into the Einstein field equations as a source and to the equations of motion as a force, and the development of a Lagrangian and variational principle for studying non-radial relativistic pulsations in stars with a solid crust.</p>
<p><i>iv)</i> Solar five-minute oscillations are a weak source of gravitational radiation. The inner part of the solar system is actually in the transition zone of the solar oscillation gravitational field, and future space-based beam detectors might be able to measure the solar "transition-zone radiation." The transition-zone gravitational field is explored for four relativistic gravity theories: a spin-zero theory (Nordstøm's theory), a spin-one theory (analogous to electromagnetism), a spin-two theory (general relativity), and a mixed spin-zero/spin-one theory (Jordan-Brans-Dicke theory). From the transition-zone gravitational field, it is possible to determine experimentally the spin content of relativistic gravity.</p>
https://thesis.library.caltech.edu/id/eprint/3230The R +ɛR² Cosmology
https://resolver.caltech.edu/CaltechTHESIS:02202013-144403198
Authors: {'items': [{'id': 'Morris-Michael-Scott', 'name': {'family': 'Morris', 'given': 'Michael Scott'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/h44f-9639
<p>This thesis presents the study of a model cosmology based on the R +ɛR² gravitational Lagrangian. It may be roughly divided into two distinct parts. First, the classical inflationary scenario is developed. Then, the formalism of quantum cosmology is employed to determine initial conditions for the classical model.</p>
<p>In the work on the classical model, the evolution equations for an isotropic and homogeneous universe are solved to exhibit both early-time inflation and a smooth transition to subsequent radiation-dominated behavior. Then perturbations on this isotropic background are evolved through the model to provide constraints on the model parameters from the observational limits on anisotropy today. This study concludes that such an inflationary model will prove a viable description for our universe if the initial Hubble parameter <i>H<sub>i</sub></i> is bounded from below, <i>H<sub>i</sub></i> > 10⁻⁵ <i>l</i><sub>Pl</sub>⁻¹, and if ɛ > 10¹¹ <i>l</i><sub>Pl</sub>².</p>
<p>In the work on the wave function, the two boundary conditions of Vilenkin ("tunneling from nothing") and Hartle and Hawking ("no boundary") are compared. The wave functions obtained are restricted to the initial edge of classical Lorentzian inflationary trajectories as distributions over initial conditions for the classical inflationary model. It is found that Vilenkin's wave function prefers the universe to undergo a great deal of inflation, whereas Hartle and Hawking's wave function prefers the universe to undergo little inflation. Finally, both boundary conditions are shown to require that inhomogeneous perturbative modes start out in their ground states.</p>https://thesis.library.caltech.edu/id/eprint/7486Novel Quantum States and Measurements
https://resolver.caltech.edu/CaltechETD:etd-06192009-150752
Authors: {'items': [{'id': 'Braunstein-Samuel-Leon', 'name': {'family': 'Braunstein', 'given': 'Samuel Leon'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/9K1B-7X39
<p>i) The quantum mechanics of higher order parametric amplifiers is studied. It is shown that these devices produce meaningful quantum states; numerical calculations are performed that demonstrate the convergence of matrix elements associated with these states. Further, the correspondence between the classical and quantum evolution for these devices is studied and the differences explained by a kind of "quantum diffusion." Finally, the possibility of producing ordinary squeezed light with these devices is noted.</p>
<p>ii) The generation of squeezed light always involves some scheme that amounts to pumping electromagnetic modes at near twice their natural frequency. When the pump is itself treated quantum mechanically, extra noise is introduced that ultimately limits the amount of squeezing achievable. Detailed calculations are carried out in this regard for the parametric amplifier. It is found that the pump's initial phase noise is responsible for this limit.</p>
<p>iii) Quantum-mechanical measurements are usually described by applying the standard quantum rules to a measurement model. They can also be described by a formalism that uses mathematical objects called Effects and Operations. These two descriptions should be equivalent. D'Espagnat has raised a question about the usage of this formalism of Effects and Operations for repeated measurements. This question is cleared up, and the source of the discrepancy is given a simple interpretation.</p>
<p>iv) Usually, an inequality that is chained becomes a weaker inequality. Chaining the Bell inequality, however, leads to stronger violations by quantum mechanics. Further, a new kind of Bell inequality, based on the information obtained in a measurement, is derived. This information Bell inequality can be used to formulate tests of local realism in very general circumstances, e.g., higher spin versions of the EPR experiment. These new inequalities yield an interpretation for the size of their violation and lead to the formulation of a hierarchy of Bell inequalities for which two-particle Bell inequalities play a special role.</p>
https://thesis.library.caltech.edu/id/eprint/2651Singularities and Horizons in the Collisions of Gravitational Waves
https://resolver.caltech.edu/CaltechTHESIS:10242013-145903390
Authors: {'items': [{'id': 'Yurtsever-Ulvi-Hamit', 'name': {'family': 'Yurtsever', 'given': 'Ulvi Hamit'}, 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/zm5n-g882
<p>This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. It is focused mainly on two fundamental questions: First, what is the general structure of the singularities and Killing-Cauchy horizons produced in the collisions of <i>exactly plane-symmetric</i> gravitational waves? Second, under what conditions will the collisions of almost-plane gravitational waves (waves with large but finite transverse sizes) produce singularities?</p>
<p>In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and that generic initial data for the colliding plane waves always produce "pure" spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction.</p>
<p>In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wavefronts; i.e., it must leave behind tails in the spacetime region through which it passes. Next, the occurrence of spacetime singularities in the collisions of almost-plane waves is investigated. It is proved that if two colliding, almost-plane gravitational waves are initially exactly plane-symmetric across a central region of sufficiently large but <i>finite</i> transverse dimensions, then their collision produces a spacetime singularity with the same local structure as in the exact-plane-wave collision. Finally, it is shown that a singularity still forms when the central regions are only approximately plane-symmetric initially. Stated more precisely, it is proved that if the colliding almost-plane waves are initially sufficiently close to being exactly plane-symmetric across a bounded central region of sufficiently large transverse dimensions, then their collision necessarily produces spacetime singularities. In this case, nothing is now known about the local and global structures of the singularities.</p>https://thesis.library.caltech.edu/id/eprint/8009Multipole moments in general relativity and dynamical perturbations of black-hole magnetospheres
https://resolver.caltech.edu/CaltechTHESIS:03172015-154851912
Authors: {'items': [{'id': 'Zhang-Xiao-He', 'name': {'family': 'Zhang', 'given': 'Xiao-He'}, 'show_email': 'NO'}]}
Year: 1990
DOI: 10.7907/ra46-aj38
<p>This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.</p>
<p>In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e<sup>+</sup>e<sup>-</sup>) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common
rest frame of the freshly created plasma and the rotating magnetic field lines. The
magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) Ω<sub>H</sub> where m is an integer and Ω<sub>H</sub> is the hole's angular velocity.</p>
https://thesis.library.caltech.edu/id/eprint/8780Properties of infrared-luminous galaxies, or, how I spent seven summer vacations
https://resolver.caltech.edu/CaltechETD:etd-05162007-161518
Authors: {'items': [{'id': 'Carico-D-P', 'name': {'family': 'Carico', 'given': 'David Paul'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/XZPT-HV21
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Galaxies selected from the IRAS database having unusually high 60 - 100µm luminosities are studied at wavelengths ranging from ~1 - 1000µm. It is found that these galaxies differ significantly from normal, optically-selected galaxies, not only in their far-infrared luminosities, but in their near-infrared properties as well. A substantial excess emission at near-infrared wavelengths is attributed to emission from hot dust, with temperatures ~500 - 1000 K. Furthermore, this hot dust emission is confined to the central nuclear regions, within characteristic scale sizes ~1 - 3 kpc. This suggests that the bulk of the infrared luminosity, and hence the processes responsible for the extreme activity in infrared-luminous galaxies, is highly localized about galaxy nuclei. High resolution images of a number of these nuclei reveals a high percentage of double-nucleus sources amongst the most luminous galaxies, giving evidence that galaxy-galaxy interactions play a significant role in the generation of high infrared luminosities.
The distribution of the mass of, and luminosity from, dust in infrared-luminous galaxies is analyzed as a function of the temperature of the dust. It is found that, in galaxies for which the entire energy distribution is dominated by emission from dust heated to a steady-state, the mass of dust scales with steady-state temperature as [...], where [...] is typically in the range 6 - 6.5. Dust continues to contribute substantially to the total luminosity up to temperatures in excess of 300 K above the temperatures responsible for the peak in the infrared luminosity. At the lowest temperatures, however, it is very difficult to constrain the contribution to the observed emission: For the galaxies studied, the observations are consistent with models in which the amount of very cold dust ranges from essentially non-existent, to the dominant component of the total dust mass.https://thesis.library.caltech.edu/id/eprint/1840Multiply connected spacetimes and closed timelike curves in semiclassical gravity
https://resolver.caltech.edu/CaltechTHESIS:08302011-113709010
Authors: {'items': [{'id': 'Klinkhammer-G-U', 'name': {'family': 'Klinkhammer', 'given': 'Gunnar Ulrich'}, 'show_email': 'NO'}]}
Year: 1992
DOI: 10.7907/694e-b162
In this thesis, we present three studies motivated by the recent interest in spacetimes with closed timelike curves ("CTC's").
First, it has been shown that certain energy conditions must be violated if spacetime is to develop CTC's. We initiate a study of whether quantum field theory permits such violations by proving that, in Minkowski spacetime, a free scalar field will satisfy the weak and strong energy conditions averaged along any complete null or timelike geodesic. We remark that in fiat, but topologically nontrivial spacetimes, the averaged weak energy condition can be violated.
Second, it has been argued that the most likely way by which Nature might prevent the creation of CTC's is a divergent vacuum polarization at the chronology
horizon where such CTC's first arise. We derive the form of the vacuum polarization of a conformal scalar field and of a spin-1/2 field near a closed null geodesic from which the null generators of a generic compactly generated chronology horizon spring forth. We show that the tensorial structure of the polarization and its degree of divergence are the same for scalar and for spin-1/2 fields and are independent
of the details of the spacetime geometry. We also show that in generic cases, there will be no cancellation of this divergence for a combination of scalar and spin-1/2 fields that has equal numbers of Fermi and Bose degrees of freedom.
Third, in anticipation of the possibility that Nature might permit CTC's, we demonstrate that for a classical body with a hard-sphere potential and no internal degrees of freedom (a "billiard ball") traveling nonrelativistically in a wormhole spacetime with CTC's, the Cauchy problem is ill-posed in a peculiar way. For certain ("dangerous") initial data, there would appear to be no self-consistent
solution to the equations of motion because the ball collides with its younger self after having traversed the wormhole. However, we show that for a wide range of dangerous and non-dangerous initial data, there is an infinity of self-consistent solutions, each involving one self-collision. No initial data are found for which
there is no self-consistent solution.
https://thesis.library.caltech.edu/id/eprint/6633Studies of stars with neutron cores and of x-ray binaries displaying quasi-periodic oscillations
https://resolver.caltech.edu/CaltechTHESIS:12042012-092833556
Authors: {'items': [{'id': 'Biehle-G-T', 'name': {'family': 'Biehle', 'given': 'Garrett T.'}, 'show_email': 'NO'}]}
Year: 1993
DOI: 10.7907/sx31-ra11
<p>This thesis contains the results of two investigations: one into the nature of stars with degenerate neutron cores and the other into the interpretation of the phenomenology of luminous low-mass X-ray binaries (LMXBs) displaying slow
quasi-periodic oscillations (QPOs) in their X-ray flux.</p>
<p> A star with a degenerate neutron core would be a red giant or supergiant. In this thesis we investigate the structure of such a supergiant, particularly examining
the energy production and seeking an identifying observational signature. This star is convective from near the photosphere down to the base of the envelope just
outside the degenerate core (radius 10 km). The star's luminosity comes from the rp-process in a convective burning region within 100 km of the base of the envelope. The convection brings fuel for the rp-process into the burning region from throughout the envelope and deposits the products of rp-burning back into the envelope, including the photosphere. After about 10^5 years, the abundances of Br, Rb, Y, and Nb at the surface of the star will be about 200 times greater than their solar abundances, and that of Mo, over 1000 times solar. A suitable observational signature would be the strong enhancement of absorption lines for these elements in the star's spectrum. As many as 10 of the nearest 100 red
supergiants (those within 5 kpc) could have neutron cores. </p>
<p> The other investigation concerns a model of rapid accretion onto an unmagnetized neutron star with radius somewhat less than 6GM/c^2. This model is applied to the phenomenology of a class of LMXBs displaying slow (∼ 6 Hz)
QPOs in X-ray flux. These sources are highly luminous (approximately Eddington) and display what appears to be three modes ("branches") of accretion. In this model, at low accretion rates, the neutron star lies within the inner edge of the accretion disk, and matter is dripped onto the neutron star from the inner edge. As the accretion rate increases, the transition from the "horizontal branch"
to the "normal branch" occurs when the disk thickens and its inner edge touches the star and forms a boundary layer. The formation of a boundary layer changes the structure of the inner disk and the spectral character of the escaping X-rays. The transition from the normal branch to the "flaring branch" occurs when the boundary layer covers the whole surface of the neutron star and radiation escapes
primarily through convective instabilities. This thesis presents an exploration of this model, with an emphasis on establishing the plausibility that a neutron star could indeed lie inside an accretion disk accreting at the observed rate and that a change of mass accretion rate could push the inner radius onto the surface of the
star. </p>
https://thesis.library.caltech.edu/id/eprint/7302Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars
https://resolver.caltech.edu/CaltechTHESIS:05092013-084229368
Authors: {'items': [{'id': 'Marković-D', 'name': {'family': 'Marković', 'given': 'Dragoljub'}, 'show_email': 'NO'}]}
Year: 1994
DOI: 10.7907/ms5q-kt36
<p>This thesis consists of three separate studies of roles that black holes might
play in our universe. </p>
<p>In the first part we formulate a statistical method for inferring the cosmological
parameters of our universe from LIGO/VIRGO measurements of the gravitational
waves produced by coalescing black-hole/neutron-star binaries. This method is
based on the cosmological distance-redshift relation, with "luminosity distances"
determined directly, and redshifts indirectly, from the gravitational waveforms.
Using the current estimates of binary coalescence rates and projected "advanced"
LIGO noise spectra, we conclude that by our method the Hubble constant should
be measurable to within an error of a few percent. The errors for the mean density
of the universe and the cosmological constant will depend strongly on the size of
the universe, varying from about 10% for a "small" universe up to and beyond
100% for a "large" universe. We further study the effects of random gravitational
lensing and find that it may strongly impair the determination of the cosmological
constant. </p>
<p>In the second part of this thesis we disprove a conjecture that black holes cannot
form in an early, inflationary era of our universe, because of a quantum-field-theory induced
instability of the black-hole horizon. This instability was supposed to arise
from the difference in temperatures of any black-hole horizon and the inflationary
cosmological horizon; it was thought that this temperature difference would make
every quantum state that is regular at the cosmological horizon be singular at
the black-hole horizon. We disprove this conjecture by explicitly constructing a
quantum vacuum state that is everywhere regular for a massless scalar field. We
further show that this quantum state has all the nice thermal properties that one
has come to expect of "good" vacuum states, both at the black-hole horizon and
at the cosmological horizon. </p>
<p>In the third part of the thesis we study the evolution and implications of a hypothetical
primordial black hole that might have found its way into the center of the
Sun or any other solar-type star. As a foundation for our analysis, we generalize
the mixing-length theory of convection to an optically thick, spherically symmetric
accretion flow (and find in passing that the radial stretching of the inflowing fluid
elements leads to a modification of the standard Schwarzschild criterion for convection).
When the accretion is that of solar matter onto the primordial hole, the
rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting
in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport
of this heat, extracts angular momentum from the inflowing gas, thereby buffering
the torus into a lower luminosity than one might have expected. As a result, the
solar surface will not be influenced noticeably by the torus's luminosity until at
most three days before the Sun is finally devoured by the black hole. As a simple
consequence, accretion onto a black hole inside the Sun cannot be an answer to
the solar neutrino puzzle. </p>
https://thesis.library.caltech.edu/id/eprint/7688Topics in general relativity : the hoop conjecture and theoretical aspects of gravitational wave detection
https://resolver.caltech.edu/CaltechETD:etd-11132006-095610
Authors: {'items': [{'email': 'eef3@cornell.edu', 'id': 'Flanagan-E-E', 'name': {'family': 'Flanagan', 'given': 'Eanna E.'}, 'show_email': 'YES'}]}
Year: 1994
DOI: 10.7907/7SW7-8076
The body of this thesis consists of four chapters (2 through 5), each of which is a paper that has been published in or submitted for publication to Physical Review D. I am the sole author of chapters 2, 3, and 4; Curt Cutler coauthored chapter 5 with me.
These four chapters deal with two topics in general relativity: the formation of horizons in nonspherical gravitational collapse (chapters 2 and 3), and some theoretical aspects of the effort to detect gravitational waves from cosmic sources (chapters 4 and 5). These four chapters were written largely for experts in the topics they cover. As an aid to general readers, I shall give in this introductory chapter some background information about chapters 2 through 5 and a nontechnical overview of their contents.https://thesis.library.caltech.edu/id/eprint/4534Searching for Black Holes and Other Massive, Compact Bodies Using the Gravitational Waves from Binary Inspirals
https://resolver.caltech.edu/CaltechTHESIS:09062017-160111338
Authors: {'items': [{'id': 'Ryan-Fintan-Danh', 'name': {'family': 'Ryan', 'given': 'Fintan Danh'}}]}
Year: 1997
DOI: 10.7907/3n38-zg42
We consider several issues involved with searching for and studying different types of compact bodies using the gravitational waves from binary inspirals. In Chapter 2, we use a radiation reaction force formalism to compute (to leading post-Newtonian order) the inspiral evolution of a circular, nonequatorial orbit around a spinning black hole. We find that an initially circular orbit remains circular under radiation reaction and is driven towards anti-alignment with the black hole's spin direction. In Chapter 3, we apply this same formalism to orbits which are elliptical as well as nonequatorial. In addition, we prove that circular orbits remain circular exactly. In Chapter 4, we show that all the multipole moments of a massive, compact body (whose gravitational field is stationary, axially symmetric, and reflection symmetric across the equatorial plane) can be determined from the gravitational waves produced by a much less massive, compact object inspiraling in a contracting circle in the equatorial plane. We show that the moments are encoded in the waves' evolution in (at least) four independent functions of the gravitational-wave frequency: the gravitational-wave energy, the precession frequency of the orbit when slightly eccentric, the precession frequency of the orbit when slightly nonequatorial, and the gravitational-wave phase evolution. In Chapter 5, we compute the structure and the multipole moments of a spinning boson star with large self-interaction. We find that only three moments are needed to specify all the star's properties, and that the pattern of moments is very different from that for black holes. In Chapter 6, we estimate how accurately a gravitational-wave detector can estimate the multipole moments of the central body from the gravitational waves produced by an inspiraling compact object. We find that, typically, a space-based detector such as LISA (as opposed to an Earth-based detector such as LIGO) is necessary to get accurate enough measurements of the multipole moments so as to search for massive, compact, non-black-hole objects. In Chapter 7, as a model for computing the full details of the gravitational waves from an orbital inspiral, we compute the scalar waves produced by a scalar charge in a circular, equatorial orbit around a body with arbitrary multipole moments.https://thesis.library.caltech.edu/id/eprint/10416Radiation Reaction in Binary Systems in General Relativity
https://resolver.caltech.edu/CaltechTHESIS:08222017-154459722
Authors: {'items': [{'id': 'Kennefick-Daniel-John', 'name': {'family': 'Kennefick', 'given': 'Daniel John'}}]}
Year: 1997
DOI: 10.7907/jzcp-a525
<p>This thesis is concerned with current problems in, and historical aspects of, the problem of radiation reaction in stellar binary systems in general relativity. Part I addresses current issues in the orbital evolution due to gravitational radiation damping of compact binaries. A particular focus is on the inspiral of small bodies orbiting large black holes, employing a perturbation formalism. In addition, the merger, at the end of the insprial, of comparable mass compact binaries, such as neutron star binaries is also discussed. The emphasis of Part I is on providing detailed descriptions of sources and signals with a view to optimising signal analysis in gravitational wave detectors, whether ground- or space-based interferometers, or resonant mass detectors.</p>
<p>Part II of the thesis examines the historical controversies surrounding the problem of gravitational waves, and gravitational radiation damping in stellar binaries. In particular, it focuses on debates in the mid 20th-century on whether binary star systems would really exhibit this type of damping and emit gravitational waves, and on the "quadrupole formula controversy" of the 1970s and 1980s, on the question whether the standard formular describing energy loss due to emission of gravitational waves was correctly derived for such systems. The study sheds light on the role of analogy in science, especially where its use is controversial, on the importance of style in physics and on the problem of identity in science, as the use of history as a rhetorical device in controversial debate is examined. The concept of the Theoretician's Regress is introduced to explain the difficulty encountered by relativists in closing debate in this controversy, which persisted in one form or another for several decades.</p>https://thesis.library.caltech.edu/id/eprint/10384Gravitational Waves from Compact Objects
https://resolver.caltech.edu/CaltechTHESIS:08302017-132619494
Authors: {'items': [{'id': 'Owen-Benjamin-James', 'name': {'family': 'Owen', 'given': 'Benjamin James'}}]}
Year: 1998
DOI: 10.7907/63nf-9z58
<p>This thesis addresses problems in the generation and detection of gravitational waves
from two types of sources: inspiraling compact binaries and rapidly rotating young
neutron stars.</p>
<p>Chapters 2 and 3 estimate the computational costs of a basic matched filtering strategy to search for inspiraling compact binaries. Chapter 2 (written in 1995) sets up the machinery for calculating costs and makes a rough estimate based on the waveforms and noise spectra available at the time. It also systematizes previously published methods of choosing the filters. Chapter 3 (written with B. S. Sathyapra kash in 1998) fine-tunes the machinery and updates the estimates of Chapter 2 using more current waveforms and noise spectra.</p>
<p>Chapter 4 (written with Hideyuki Tagoshi and Akira Ohashi) concerns the post Newtonian generation of gravitational waveforms from inspiraling compact binaries whose component objects spin about their own axes. It lays out a method of cal culating post-Newtonian spin effects and calculates the lowest-order such effect not previously known (the second-post-Newtonian spin-orbit contribution to the wave forms in the absence of precession).</p>
<p>Chapters 5 and 6 concern the Chandrasekhar-Friedman-Schutz (CFS) gravitational radiation instability as it applies to the τ-modes of rapidly rotating young neutron stars. Chapter 5 (written with Lee Lindblom and Sharon M. Morsink) com putes the viscous damping and gravitational radiation timescales of the τ-modes and shows that viscosity does not suppress the CFS instability in hot young neutron stars. Chapter 6 (written with Lee Lindblom, Curt Cutler, Bernard F. Schutz, Alberto Vecchio, and Nils Andersson) computes approximate gravitational waveforms from young neutron stars spinning down due to the τ-mode instability and estimates that these gravitational waves can be detected by the "enhanced" LIGO interferometers if a suitable data analysis strategy is developed.</p>https://thesis.library.caltech.edu/id/eprint/10402Gravitational-Wave Astronomy: Aspects of the Theory of Binary Sources and Interferometric Detectors
https://resolver.caltech.edu/CaltechTHESIS:08302017-134937434
Authors: {'items': [{'id': 'Hughes-Scott-Alexander', 'name': {'family': 'Hughes', 'given': 'Scott Alexander'}}]}
Year: 1998
DOI: 10.7907/smxp-aw47
<p>This thesis presents a study of several problems and issues in the nascent field of gravitational-wave astronomy. Multi-kilometer baseline interferometers are being built in the United States [the LIGO (Laser Interferometer Gravitational-wave Observatory) project] and similar projects are underway in Europe (the VIRGO and GE0600 projects) and Japan (the TAMA300 project). LIGO will begin operations very soon (the first science run is scheduled for 2002), and detectors in other countries will begin soon as well. We are thus about 5 years from using gravitational waves as a new window to probe astrophysical processes in the universe.</p>
<p>Chapters 2, 3, and 4 of this thesis study gravitational waves from coalescences of compact binaries. Chapters 2 and 3 are a detailed examination, in collaboration with Éanna É. Flanagan, of binary black hole (BBH) coalescences. The birth rate of BBH systems in the universe is highly uncertain, so it is not immediately apparent how relevant they are to gravitational-wave astronomy. If such systems do in fact exist, we find that they will be visible to extremely large distances, far greater than the distances to which binary neutron star systems, for example, will be visible. This heightened visibility may compensate for the possible dearth of such binaries, making them an extremely important and interesting source. We suggest ways in which numerical modeling of BBHs may aid gravitational-wave data analysis, and techniques that can be used in BBH event searches and waveform analysis. Chapter 4 analyzes the measurement of gravitational waves from the final merger of binary neutron star systems. Such waves depend on details of the composition of neutron stars, such as their equation of state, and may be driven by hydrodynamic and nuclear processes that occur in the final merger. Unfortunately, these waves are emitted at high frequencies where LIGO type detectors have poor sensitivity. Measuring such waves will require specialty "narrow-band" detectors. In this chapter, I present an algorithm for optimally configuring a network of multiple LIGO-type and narrow-band detectors to measure these merger waves. I find that improved
theoretical modeling of the final merger will play an important role in designing such networks and in the analysis of their data. In Chapter 5, in collaboration with Patrick R. Brady, I analyze the stability of binary neutron star systems as they coalesce. Some rather controversial numerical calculations have found that neutron stars in binary systems are rendered unstable by their companion, and may collapse into black holes long before their final merger. This would have a huge impact on the gravitational waves such systems emit. The claimed effect is first-order in a particular expansion. Motivated by this claim, Brady and I perform a first-order expansion of the fluid and field equations of general relativity, in the limit in which one star is much smaller than the other. We find that no such effect can exist. Finally, Chapter 6 is an analysis, in collaboration with Kip S. Thorne, of seismic gravity-gradient noise, a noise source that may be of concern to future detector designs. This noise source arises from fluctuations in the density of the earth near and below a LIGO-type interferometer's test masses. It is gravitational in origin, and thus cannot be shielded. By carefully studying the geological structures in the earth near the two LIGO sites, considering the propagation of elastodynamic waves in such structures, and computing the gravitational fluctuations such waves cause, we find seismic gravity-gradient noise is likely to become unavoidable at frequencies below roughly 5 Hertz. This has strong implications on plans to improve the low frequency sensitivity of the LIGO detectors.</p>
https://thesis.library.caltech.edu/id/eprint/10403Topics in Physics and Astrophysics of LIGO
https://resolver.caltech.edu/CaltechTHESIS:08292017-115000442
Authors: {'items': [{'id': 'Levin-Yuri', 'name': {'family': 'Levin', 'given': 'Yuri'}}]}
Year: 1999
DOI: 10.7907/ped8-ec41
<p>This thesis deals with three topics, all of which are related to the generation or detection of gravitational waves:</p>
<p>(I) The Standard Quantum Limit (SQL) for LIGO and Quantum Non demolition (QND) measurements, which allow one to overcome the SQL. Two particular QND measurement schemes are considered: (i) a Speed Meter, in which a small Fabry-Perot cavity attached to a LIGO test mass produces a phase shift proportional to the test mass's speed; and (ii) the Braginsky-Khalili nonlinear meter (BK-meter), in which a gravity-wave-induced motion of the nodes of the light beam inside a LIGO optical cavity is read out using a nonlinear medium which couples light to a microwave readout device. Our analysis shows that</p>
<p>(a) Using the Speed Meter one can perform naturally a broad-band QND measurement of a force acting on the test mass; however, this requires circulating light power which is unrealistically high for LIGO.</p>
<p>(b) The BK-meter can provide a natural way to perform a narrow-band QND measurement of a force acting on the mirrors of the optical cavity.</p>
<p>While neither of these QND measurement schemes can be immediately imple mented for LIGO, they might provide conceptual steps towards the design of a practical QND interferometer.</p>
<p>(II) Mechanical thermal noise in LIGO. We develop a new method of calcu lating thermal noise in mechanical systems, which is based on a direct application of the Fluctuation-Dissipation theorem. This method is capable of handling mechanical systems with inhomogeneous dissipation, by contrast with previous met hods (based on decomposing motion of the system into normal modes), which give incorrect results when the dissipation is inhomogeneous.</p>
<p>We apply our direct method to an internal thermal noise in LIGO test masses.
We find that:</p>
<p>(a) The test-mass surface defects will make a larger contribution to thermal noise than was previously inferred by combining the (incorrect) mode-sum met hod with measurements of the Q's of the test masses' modes.</p>
<p>(b)Our direct met hod is more precise and computationally less expensive for small beam sizes than the previous mode-sum method.</p>
<p>We also apply our direct method of analysis to suspension thermal noise in LIGO. We find that by careful positioning the laser beam spot on the mirror face and by monitoring independently the motion of the suspension wires, it may be possible to reduce the suspension thermal noise by a factor ~ 100 in spectral density.</p>
<p>(III) R-modes in Neutron Stars (NS) in Low-Mass X-ray Binaries (LMXBs). We study the suggestion that the accretion of gas onto a neutron star in an LMXB triggers an instability in which the star's r-modes are amplified by gravitational-wave emission. We find that if this is the case, then the subsequent neutron-star evolution depends critically on whether the neutron-star viscosity decreases with temperature, or is temperature-independent.</p>
<p>In the former case, the Neutron Star goes through runaway cycles of rapid (~ 1 month) heating-rapid (~ 1 month) spindown-slow (~ 10<sup>5</sup> years) cooling-slow (~ 10<sup>6</sup> years) spin-up. In this scenario the duration of the gravitational radiation from the unstable r-modes is so short that even LIGO-III interferometers are unlikely to be able to catch a single LMXB in the throes of its gravitational-wave emission.</p>
<p>In the latter (temperature-independent) case, however, the Neutron Star probably settles down into an equilibrium state with constant spin rate and temperature, and becomes a steady emitter of gravitational waves, which might be detectible by LIGO II interferometers.</p>
<p>All the capters in this thesis, except the introductory chapter I, have been published or are in press.</p>
https://thesis.library.caltech.edu/id/eprint/10396From the Big Bang to Tumbleweeds: Analysis of Signals from Relic Gravitons, Neutron Stars, and Terrestrial Gravitational Noise in Gravitational Wave Detectors
https://resolver.caltech.edu/CaltechTHESIS:08302017-093459499
Authors: {'items': [{'id': 'Creighton-Teviet-David', 'name': {'family': 'Creighton', 'given': 'Teviet David'}}]}
Year: 2000
DOI: 10.7907/6xcj-0z64
<p>This dissertation explores three separate issues in the field of gravitational-wave astronomy: optimal detection algorithms for quasi-periodic signals, gravitational-wave signatures of the equation of state in the early universe, and local Newtonian gravitational noise from nearby airborne masses as possible contaminants of the gravitational-wave signal.</p>
<p>Continuous quasi-periodic signals are waveforms that maintain phase coherence over times longer than practical observation times, although the phase may drift in a way that can be modeled with few parameters. Sensitivity to such signals is limited by the computational cost of the analysis, especially since the detection algorithm must search over many values of the parameters in the phase model; it is therefore crucial to develop computationally efficient search strategies. One such strategy is a hierarchical stack search: a technique combining coherent phase corrections on short stretches of data with incoherent frequency drift corrections among several such stretches. The procedure is repeated at least twice, with each pass increasing the confidence in any putative signal. This dissertation discusses how to choose parameter values and observation times for greatest sensitivity, and shows how several astrophysically interesting sources may be detectable by this method.</p>
<p>A background of gravitational waves originating in the Big Bang or a pre-Big-Bang collapsing universe will not thermalize in any cosmological epoch, but may be amplified by an intermediate epoch when the wavelengths were stretched outside the Hubble radius. The present-day spectral index is related simply and generically to the initial spectrum, and to the cosmological equation of state at the beginning and end of the intermediate epoch. This dissertation derives this relation, and compares it to related but more model-specific formulae in the current literature.</p>
<p>Finally, this dissertation considers two atmospheric sources of background Newtonian gravitational noise (infrasonic pressure waves and wind-advected density perturbations), and two sources of transient Newtonian gravitational signals (atmospheric shockwaves and massive airborne bodies, especially tumbleweeds). Neither background noise source will exceed the noise floor for advanced detectors, but sonic booms and wind-borne debris striking the detector can both produce detectable spurious signals through their gravitational effects. Possible corrective measures arc discussed.</p>https://thesis.library.caltech.edu/id/eprint/10400Topics in General Relativity: Binary Black Holes and Hyperbolic Formulations of Einstein's Equations
https://resolver.caltech.edu/CaltechTHESIS:01202012-112836824
Authors: {'items': [{'id': 'Alvi-Kashif-Siddiq', 'name': {'family': 'Alvi', 'given': 'Kashif Siddiq'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/5S0S-MF65
<p>This thesis consists of three projects in general relativity on topics related to binary black holes
and the gravitational waves they emit. The first project involves calculating a four-metric that is an approximate solution to Einstein's equations representing two widely separated nonrotating black holes in a circular orbit. This metric is constructed by matching a post-Newtonian metric to
two tidally distorted Schwarzschild metrics using the framework of matched asymptotic expansions. The four-metric presented here provides physically realistic initial data that are tied to the binary's inspiral phase and can be evolved numerically to determine the gravitational wave output during the late stages of inspiral as well as the merger.</p>
<p>The second project is on the tidal interaction of binary black holes during the inspiral phase. The holes' tidal distortion results in the flow of energy and angular momentum into or out of the holes in a process analogous to Newtonian tidal friction in a planet-moon system. The changes in the black holes' masses, spins, and horizon areas during inspiral are calculated for a circular binary with holes of possibly comparable masses. The absorption or emission of energy and angular momentum by the holes is shown to have a negligible influence on the binary 's orbital evolution when the holes have comparable masses. The tidal-interaction analysis presented in this thesis is applicable to a black hole in a binary with any companion body (e.g., a neutron star) that is well separated from
the hole.</p>
<p>The final project is on first-order hyperbolic formulations of Einstein's equations, which are promising as a basis for numerical simulation of binary black holes. This thesis presents two first-order symmetrizable hyperbolic systems that include the lapse and shift as dynamical fields and have only physical characteristic speeds. The first system may be useful in numerical work; the second system allows one to show that any solution to Einstein's equations in any gauge can be obtained
using hyperbolic evolution of the entire metric, including the gauge fields.</p>https://thesis.library.caltech.edu/id/eprint/6771Modeling and Detecting Gravitational Waves from Compact Stellar Objects
https://resolver.caltech.edu/CaltechETD:etd-05292002-113750
Authors: {'items': [{'email': 'vallis@vallis.org', 'id': 'Vallisneri-Michele', 'name': {'family': 'Vallisneri', 'given': 'Michele'}, 'orcid': '0000-0002-4162-0033', 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/JN6M-BW40
<p>In the next few years, the first detections of gravity-wave signals using Earth-based interferometric detectors will begin to provide precious new information about the structure, dynamics, and evolution of compact bodies, such as neutron stars and black holes, both isolated and in binary systems. The intrinsic weakness of gravity-wave signals requires a proactive approach to modeling the prospective sources and anticipating the shape of the signals that we seek to detect. Full-blown 3-D numerical simulations of the sources are playing and will play an important role in planning the gravity-wave data-analysis effort. This thesis explores the interplay between numerical source modeling and data analysis, looking closely at three case studies.</p>
<p>1. I evaluate the prospects for extracting equation-of-state information from neutron-star tidal disruption in neutron-star–black-hole binaries with LIGO-II, and I estimate that the observation of disrupting systems at distances that yield about one event per year should allow the determination of the neutron-star radius to about 15%, which compares favorably to the currently available electromagnetic determinations.</p>
<p>2. In collaboration with Lee Lindblom and Joel Tohline, I perform numerical simulations of the nonlinear dynamics of the <i>r</i>-mode instability in young, rapidly spinning neutron stars, and I find evidence that nonlinear couplings to other modes will not pose a significant limitation to the growth of the <i>r</i>-mode amplitude.</p>
<p>3. In collaboration with Alessandra Buonanno and Yanbei Chen, I study the problem of detecting gravity waves from solar-mass black-hole–black-hole binaries with LIGO-I, and I construct two families of <i>detection</i> templates that address the inadequacy of standard post-Newtonian theory to predict reliable waveforms for these systems.</p>
https://thesis.library.caltech.edu/id/eprint/2226Dynamical Stability of Nascent Neutron Stars
https://resolver.caltech.edu/CaltechTHESIS:03112014-101628149
Authors: {'items': [{'email': 'ytliu@illinois.edu', 'id': 'Liu-Yuk-Tung', 'name': {'family': 'Liu', 'given': 'Yuk Tung'}, 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/61ZS-XQ28
<p>This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the
accretion induced collapse of rapidly rotating white dwarfs.</p>
<p>Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are
constructed by assuming that the neutron stars have the same masses, angular momenta, and specific
angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is
rapidly rotating, the collapsed object will contain a high density central core of size about 20 km,
surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis.
The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars
is all found to be less than 0.27.</p>
<p>Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the
linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of
the star is greater than the critical value β<sub>d</sub> ≈ 0.25. It is expected that the unstable mode will
persist until a substantial amount of angular momentum is carried away by gravitational radiation.
The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect
them unless the event rate is greater than 10<sup>-6</sup>/year/galaxy.</p>
<p>All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3
are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic
effects on the structure of these neutron stars. New techniques are developed and used to construct
neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models
are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat
smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than
the Newtonian result (0.26). However, relativistic effects will also change the critical value β<sub>d</sub>. A
detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects
on the dynamical stability of these neutron stars.</p>https://thesis.library.caltech.edu/id/eprint/8122Topics of LIGO Physics: Quantum Noise in Advanced Interferometers and Template Banks for Compact-Binary Inspirals
https://resolver.caltech.edu/CaltechETD:etd-05302003-044325
Authors: {'items': [{'email': 'yanbei@tapir.caltech.edu', 'id': 'Chen-Yanbei', 'name': {'family': 'Chen', 'given': 'Yanbei'}, 'orcid': '0000-0002-9730-9463', 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/VQH0-QA78
This thesis deals with the planning for advanced interferometric gravitational-wave detectors, as well as the detection of inspiral waves using first-generation interferometers.
In Chapters 2 -- 4 (in collaboration with Alessandra Buonanno), the the signal recycling interferometer proposed for LIGO-II is studied in the two-photon formalism. This study reveals the optical spring effect, which allows the interferometer to beat the standard quantum limit, while in the same time introduces a dynamical instability. A classical control system is designed to suppress this instability. In Chapter 5 (in collaboration with Alessandra Buonanno and Nergis Mavalvala), the quantum noise in heterodyne readout schemes for advanced interferometers is studied. In Chapter 6 (in collaboration with Patricia Purdue), a QND Speed-Meter interferometer with Michelson topology is proposed, analyzed and shown to be a promising candidate for third-generation interferometers (LIGO-III or EURO). This design requires adding a kilometer-scale cavity into the interferometer. In Chapter 7, Sagnac interferometers are analyzed and shown to exhibit a similar broadband QND performance without the need of additional cavity --- as expected since these interferometers are sensitive only to time-dependent mirror displacement, and are automatic speed meters.
In Chapter 8 (in collaboration with Alessandra Buonanno and Michele Vallisneri), the Post-Newtonian (PN) breakdown at late-stage inspirals of non-spinning binary black holes is studied. We propose the use of Detection Template Families (DTFs) --- extensions of ordinary PN templates that can mimic all different PN waveforms and hence are plausible to catch the real waveform, yet do not provide straightforward parameter estimation. In Chapter 9 (in collaboration with Alessandra Buonanno and Michele Vallisneri), binaries carrying spins are studied using an adiabatic PN model. Based on features of the precession dynamics, we construct a DTF, using a modified Apostolatos' ansatz, that can mimic the modulated waveforms reasonably well, while keeping a small number of parameters to be searched over one by one, with the rest searched over automatically. We also propose a (computationally) plausible way of searching over the entire physical parameter space of neutron-star--black-hole binaries.https://thesis.library.caltech.edu/id/eprint/2286Topics in LIGO-Related Physics: Interferometric Speed Meters and Tidal Work
https://resolver.caltech.edu/CaltechTHESIS:03062014-090212906
Authors: {'items': [{'id': 'Purdue-Patricia-Marie', 'name': {'family': 'Purdue', 'given': 'Patricia Marie'}, 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/0YKJ-SW34
<p>In the quest to develop viable designs for third-generation optical interferometric gravitational-wave
detectors, one strategy is to monitor the relative momentum or speed of the test-mass mirrors,
rather than monitoring their relative position. The most straightforward design for a speed-meter
interferometer that accomplishes this is described and analyzed in Chapter 2. This design (due
to Braginsky, Gorodetsky, Khalili, and Thorne) is analogous to a microwave-cavity speed meter
conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter
and the optical interferometric speed meter is developed and used to show (in accord with the speed
being a quantum nondemolition observable) that in principle the interferometric speed meter can
beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an
arbitrarily wide range of frequencies . However, in practice, to reach or beat the SQL, this specific
speed meter requires exorbitantly high input light power. The physical reason for this is explored,
along with other issues such as constraints on performance due to optical dissipation.</p>
<p>Chapter 3 proposes a more sophisticated version of a speed meter. This new design requires
only a modest input power and appears to be a fully practical candidate for third-generation LIGO.
It can beat the SQL (the approximate sensitivity of second-generation LIGO interferometers) over
a broad range of frequencies (~ 10 to 100 Hz in practice) by a factor h/h<sub>SQL</sub> ~ √W^(SQL)_(circ)/W<sub>circ</sub>.
Here W<sub>circ</sub> is the light power circulating in the interferometer arms and W<sub>SQL</sub> ≃ 800 kW is the
circulating power required to beat the SQL at 100 Hz (the LIGO-II power). If squeezed vacuum
(with a power-squeeze factor e<sup>-2R</sup>) is injected into the interferometer's output port, the SQL can
be beat with a much reduced laser power: h/h<sub>SQL</sub> ~ √W^(SQL)_(circ)/W<sub>circ</sub>e<sup>-2R</sup>. For realistic parameters
(e<sup>-2R</sup> ≃ 10 and W<sub>circ</sub> ≃ 800 to 2000 kW), the SQL can be beat by a factor ~ 3 to 4 from 10
to 100 Hz. [However, as the power increases in these expressions, the speed meter becomes more
narrow band; additional power and re-optimization of some parameters are required to maintain the
wide band.] By performing frequency-dependent homodyne detection on the output (with the aid
of two kilometer-scale filter cavities), one can markedly improve the interferometer's sensitivity at
frequencies above 100 Hz.</p>
<p>Chapters 2 and 3 are part of an ongoing effort to develop a practical variant of an interferometric
speed meter and to combine the speed meter concept with other ideas to yield a promising third-
generation interferometric gravitational-wave detector that entails low laser power.</p>
<p>Chapter 4 is a contribution to the foundations for analyzing sources of gravitational waves for
LIGO. Specifically, it presents an analysis of the tidal work done on a self-gravitating body (e.g., a
neutron star or black hole) in an external tidal field (e.g., that of a binary companion). The change
in the mass-energy of the body as a result of the tidal work, or "tidal heating," is analyzed using the
Landau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the
work done on the body is gauge invariant, while the body-tidal-field interaction energy contained
within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian
theory, where the interaction energy is shown to depend on how one localizes gravitational energy,
but the work done on the body is independent of that localization. These conclusions play a role
in analyses, by others, of the dynamics and stability of the inspiraling neutron-star binaries whose
gravitational waves are likely to be seen and studied by LIGO.</p>https://thesis.library.caltech.edu/id/eprint/8107Topics in Gravitational-Wave Astronomy
https://resolver.caltech.edu/CaltechETD:etd-08052003-161044
Authors: {'items': [{'email': 'richard.oshaughnessy@ligo.org', 'id': "O'Shaughnessy-Richard-William", 'name': {'family': "O'Shaughnessy", 'given': 'Richard William'}, 'orcid': '0000-0001-5832-8517', 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/4C1K-VZ17
<p>Both the Laser Interferometer Gravitational Wave Observatory (LIGO) and the Laser Interferometer Space Antenna (LISA) will over the next decade detect gravitational waves emitted by the motion of compact objects (e.g. black hole and neutron star binaries). This thesis presents methods to improve (i) LIGO detector quality, (ii) our knowledge of waveforms for certain LIGO and LISA sources, and (iii) models for the rate of detectability of a particular LISA source.</p>
<p>1) Plunge of compact object into a supermassive black hole: LISA should detect many inspirals of compact objects into supermassive black holes (~ 10⁵-10⁷ M<sub>⊙</sub>). Since the inspiral of each compact object terminates shortly after the inspiralling object reaches its last stable orbit, the late-stage inspiral waveform provides insight into the location of the last stable orbit and strong-field relativity. I discovered that while LISA will easily see the overall inspiral (consisting of many cycles before plunge), the present LISA design will just miss detecting the waves emitted from the transition from inspiral to plunge.</p>
<p>2) Scheme to reduce thermoelastic noise in advanced LIGO: After its first upgrade, LIGO will have its sensitivity limited by thermoelastic noise. [Thermoelastic noise occurs because milimeter-scale thermal fluctuations in the mirror bulk expand and contract, causing the mirror surface to shimmer.] The interferometer's sensitivity could be enhanced substantially by reducing thermoelastic noise. In collaboration with Kip Thorne, Erika d'Ambrosio, Sergey Vyatchanin, and Sergey Strigin, I developed a proposal to reduce thermoelastic noise in advanced-LIGO by switching the LIGO cavity optics from simple spherical mirrors to a new, Mexican-hat shape.</p>
<p>3) Geometric-optics-based analysis of stability of symmetric-hyperbolic formulations of Einstein's equations: Einstein's equations must be evolved numerically to predict accurate waveforms for the late stages of binary black hole inspiral and merger. But no matter which representation of Einstein's equations is used, numerical simulations rarely run long. For examle, for first-order symmetric-hyperbolic (FOSH) formulations of Einstein's evolution equations, sometimes exact but unphysical solutions grow so large that the evolution fails. For FOSH formulations, I found easily-understood solutions (wave packets) and used them to predict which formulations will be particularly ill-behaved.</p>https://thesis.library.caltech.edu/id/eprint/3017Topics of LIGO Physics: Template Banks for the Inspiral of Precessing, Compact Binaries, and Design of the Signal-Recycling Cavity for Advanced LIGO
https://resolver.caltech.edu/CaltechETD:etd-05242006-025220
Authors: {'items': [{'email': 'ypan@tapir.caltech.edu', 'id': 'Pan-Yi', 'name': {'family': 'Pan', 'given': 'Yi'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/TJB1-PQ24
<p>In the next decade, the detection of gravitational-wave signals by ground-based laser interferometric detectors (e.g., the Laser Interferometer Gravitational-Wave Observatory, or LIGO) will provide new information on the structure and dynamics of compact objects such as neutron stars (NS) and black holes (BH), both isolated and in binary systems. Efforts to detect the intrinsically weak gravitational-wave signals involve the development of high-quality detectors, the precise modeling of expected signals, and the development of efficient data analysis techniques. This thesis concerns two topics in these areas: methods to detect signals from the inspiral of precessing NS-BH and BH-BH binaries, and the design of the signal-recycling cavity for Advanced LIGO (the second generation LIGO detector).</p>
<p>The detection of signals from the inspiral of precessing binaries using the standard matched filter technique, is complicated by the large number (12 at least) of parameters required to describe the complex orbital-precession dynamics of the binary and the consequent modulations of the gravitational-wave signals. To extract these signals from the noisy detector output requires a discrete bank of a huge number of signal templates that cover the 12-dimensional parameter space; and processing data with all these templates requires computational power far exceeding what is available with current technology. To solve this problem, Buonanno, Chen, and Vallisneri (BCV) proposed the use of detection template families (DTFs) --- phenomenological templates that are capable of mimicking rather accurately the inspiral waveform calculated by the post-Newtonian (PN) approach, while having a simpler functional form to reduce the computational cost. In particular, BCV proposed the so called BCV2 DTF for the precessing-binary inspiral, which has 12 parameters (most of them phenomenological). Of these, 8 are extrinsic parameters that can be searched over analytically, and only four of them are intrinsic parameters that need be searched over in a numerical one-by-one manner. The signal-matching efficiency of the BCV2 DTF has been shown to be satisfactory for signals from comparable mass BH-BH binaries.</p>
<p>In Chapter 2 (in collaboration with Alessandra Buonanno, Yanbei Chen, Hideyuki Tagoshi, and Michele Vallisneri), I test the signal-matching efficiency of the BCV2 DTF for signals from a wide sample of precessing BH-BH and NS-BH binaries that covers the parameter range of interest for LIGO and other ground-based gravitational-wave detectors, and I study the mapping between the physical and phenomenological parameters. My colleagues and I calculate the template-match metric, propose the template-placement strategy in the intrinsic parameter space and estimate the number of templates needed (and thus equivalently the computational cost) to cover the parameter space. We also propose a so called BCV2P DTF that replaces the phenomenological parameters in the BCV2 DTF by physical parameters, which can be used to estimate the actual parameters of the binary that emitted any detected signal.</p>
<p>In Chapters 3 and 4 (in collaboration with Alessandra Buonanno, Yanbei Chen, and Michele Vallisneri), I investigate a physical template family (PTF) suggested by BCV. This PTF uses the most accurate known waveforms for inspiraling, precessing binaries (the adiabatic PN waveforms), formulated using a new precessing convention such that five parameters become extrinsic. PTF has the obvious advantages over the DTFs of a perfect match with target signals, a lower false-alarm rate at fixed threshold, and an ability to directly estimate the physical parameters of any detected signal.</p>
<p>In Chapter 3, we focus on the simpler single-spin binaries in which only four parameters out of nine remain intrinsic. We propose a two-stage scheme to search over the five extrinsic parameters quickly, and investigate the false-alarm statistics in each of the two stages. We define and calculate the metric of the full template space, and the projected metric and average metric of the intrinsic parameter subspace, and use these metrics to develop the method of template placement. Finally, we estimate that the number of templates needed to detect single-spin binary inspirals is within the reach of the current available computational power.</p>
<p>In Chapter 4, we generalize the use of the single-spin PTF to double-spin binaries, based on the fact that most double-spin binaries have similar dynamics to the single-spin ones. Since the PTF in this case is, strictly speaking, only quasi-physical, we test and eventually find satisfactory signal-matching performance. We also investigate, both analytically and numerically, the difference between the single-spin and double-spin dynamics, and gain an intuition into where in the parameter space the PTF works well. We estimate the number of templates needed to cover all BH-BH and NS-BH binaries of interest to ground-based detectors, which turns out to be roughly at the limit of currently available computational power. Since the PTF is not exactly physical for double-spin binaries, it introduces systematic errors in parameter estimation. We investigate these, and find that they are either comparable to or overwhelmed by statistical errors, for events with moderate signal-to-noise ratio. BCV and I are currently systematically investigating parameter estimation with the PTF.</p>
<p>The second part of this thesis concerns the design of the signal-recycling cavity for Advanced LIGO. In the planned Advanced-LIGO-detector upgrades from the first-generation LIGO, a signal-recycling mirror (SRM) is introduced at the dark output port. This SRM forms a signal-recycling cavity (SRC) with the input test masses. This signal-recycling design offers several advantages and brings new physics to LIGO. However, there is a problem in the current design of the SRC: the SRC is nearly degenerate, i.e., it does not distinguish transverse optical modes; and as a result, mode coupling due to mirror deformation will strongly reduce the optical power in the fundamental mode, and thus reduce the signal strength, which is roughly proportional to it.</p>
<p>In Chapter 5, I investigate this problem using a numerical simulation of the propagation of the optical field in an Advanced LIGO interferometer. I find that if the current degenerate design for the SRC is used, there will be a serious and perhaps unattainable constraint on the magnitude of mirror deformations, in order to keep the reduction of signal-to-noise ratio below a few percent. This conclusion is consistent with previous order of magnitude estimates. This constraint poses practical difficulties on the quality of mirror polishing and the control of thermal aberration of the mirrors. Based on my simulation results, for a range of degeneracies of the SRC, I find the optimal level of degeneracy, which minimizes the reduction of signal-to-noise ratio. That optimum is nearly non-degenerate. I also discuss possible modifications to the current design that can achieve this optimal degeneracy.</p>https://thesis.library.caltech.edu/id/eprint/2007Topics in Numerical Relativity: The Periodic Standing-Wave Approximation, the Stability of Constraints in Free Evolution, and the Spin of Dynamical Black Holes
https://resolver.caltech.edu/CaltechETD:etd-05252007-143511
Authors: {'items': [{'email': 'owen@tapir.caltech.edu', 'id': 'Owen-Robert-Philip', 'name': {'family': 'Owen', 'given': 'Robert Philip'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/464A-4Y76
<p>This thesis concerns numerical relativity, the attempt to study Einstein's theory of gravitation using numerical discretization. The goal of the field, the study of gravitational dynamics in cases where symmetry reduction or perturbation theory are not possible, finally seems to be coming to fruition, at least for the archetypal problem of the inspiral and coalescence of binary black hole systems. This thesis presents three episodes that each bear some relationship to this story.</p>
<p>Chapters 2 and 3 present previously published work in collaboration with Richard Price and others on the so-called periodic standing-wave (PSW) approximation for binary inspiral. The approximation is to balance outgoing radiation with incoming radiation, stabilizing the orbit and making the problem stationary in a rotating frame. Chapters 2 and 3 apply the method to the problem of co-orbiting charges coupled to a nonlinear scalar field in three dimensions.</p>
<p>Chapters 4, 5, and 6 concern the stability of constraint fields in conventional numerical relativity simulations. Chapter 4 (also previously published work, in collaboration with the Caltech numerical relativity group, along with Michael Holst and Lawrence Kidder) presents a method for immediately correcting violations of constraints after they have arisen. Chapters 5 and 6 present methods to "damp" away constraint violations dynamically in two specific contexts. Chapter 5 (previously published work in collaboration with the Caltech numerical relativity group and Lawrence Kidder) presents a first-order linearly degenerate symmetric hyperbolic representation of Einstein's equations in generalized harmonic gauge. A representation is presented that stabilizes all constraints, including those that appear when the system is written in first-order form. Chapter 6 presents a generalization of the Kidder-Scheel-Teukolsky evolution systems that provides much-improved stability. This is investigated with numerical simulations of a single black hole spacetime.</p>
<p>Finally, chapter 7 presents work in progress to implement code to calculate the spin of black holes in numerical simulations. This requires a well-defined generalization of the concept of "rotation generators" on topological two-spheres that may not have any true Killing vectors. I present a new method for defining these fields, and results of a numerical code that computes them.</p>https://thesis.library.caltech.edu/id/eprint/2073Topics in Gravitational-Wave Physics
https://resolver.caltech.edu/CaltechETD:etd-05232007-115433
Authors: {'items': [{'email': 'geoffrey4444@gmail.com', 'id': 'Lovelace-Geoffrey-Mark', 'name': {'family': 'Lovelace', 'given': 'Geoffrey Mark'}, 'orcid': '0000-0002-7084-1070', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/94TE-3B59
<p>Together with ongoing experimental efforts to detect gravitational waves, several fronts of theoretical research are presently being pursued, including second-generation detector design, data analysis, and numerical-relativity simulations of sources. This thesis presents a study in each of these topics: i) The noise in the most sensitive frequency bands in second-generation ground-based gravitational-wave interferometers is dominated by the thermal noise of the test masses. One way to reduce test-mass thermal noise is to modify shape of the laser beam so that it better averages over the thermal fluctuations. When edge effects are neglected, the test-mass thermal noise is related to the beam shape by simple scaling laws. This thesis presents a rigorous derivation of these laws, along with estimates of the errors made by neglecting edge effects. ii) An important class of gravitational-wave sources for space-based gravitational-wave interferometers is extreme-mass-ratio inspirals (EMRIs). These are binaries in which an object of a few solar masses spirals into a (typically million-solar-mass) supermassive black hole (or, if any exist, other type of massive body). Ryan (1995) proved that, under certain simplifying assumptions, the spacetime geometry is redundantly encoded in EMRI waves. One of Ryan's assumptions was negligible tidal coupling. After first finding that only the time-varying part of the induced tide is unambiguously defined when the central body is a black hole, this thesis extends Ryan's theorem by showing that both the spacetime geometry and details of the tidal coupling are encoded in EMRI waves. iii) Merging black holes with comparable masses are important sources of gravitational waves for ground-based detectors. The gravitational waves near the time of merger can only be predicted by numerically solving the Einstein equations. Initial data in numerical simulations must contain the desired physical content but also satisfy the Einstein constraint equations. But conventional binary-black-hole initial data has physical flaws: a nonzero orbital eccentricity and an initial, unphysical pulse of spurious gravitational radiation. Using the Caltech-Cornell pseudospectral code, this thesis develops and implements methods to reduce both of these effects.</p>https://thesis.library.caltech.edu/id/eprint/1987Topics in Gravitational Physics: Tidal Coupling in Gravitational Wave Searches and Mach’s Principle
https://resolver.caltech.edu/CaltechETD:etd-05212007-004257
Authors: {'items': [{'id': 'Fang-Hua', 'name': {'family': 'Fang', 'given': 'Hua'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/D99H-J577
<p>The gravitational waves emitted by a compact object inspirling into a massive central body (e.g., a massive black hole) contain exquisite information about the spacetime geometry around that body and the tidal interaction (energy and angular momentum transfer) between the body and the inspiraling object's orbit. The first part (chapter 2--4) of this thesis studies several topics in the frame work of gravitation-wave search. In chapter 2 (in collaboration with G. Lovelace), we study the tidal interaction between a non-rotating black hole and circularly orbiting moon. Our analysis shows that the static induced quadrupole moment of the black hole is inherently ambiguous. In chapter 3, we give a survey of initial explorations of the prospects for using Advanced LIGO to detect gravitational waves from intermediate-mass-ratio inspirals (IMRIs))---analogous to the extreme-mass-ratio inspirals (EMRIs) targeted by LISA. We describe initial estimates of the detection range and the number of IMRI wave cycles in the Advanced LIGO band. We also give a detailed analysis of Advanced LIGO's accuracy for measuring the tide-induced energy transfer between the central black hole and the orbit. In chapter 4 (in collaboration with S. Babak, J. R. Gair, K. Glampedakis, and S. Hughes), we describe a new waveform-generating scheme in the context of LISA's data analysis for EMRI waves. The result is a family of "Numerical Kludge" waveforms, which share remarkable agreement with the more rigorous, but more computational-intensive Teukolsky-based waveforms.</p>
<p>The second part (chapter 5) of this thesis (in collaboration with K. S. Thorne) discusses another prediction from general relativity, the dragging of inertial frames, in connection with Mach's principle. We idealize our universe as a homogeneous, isotropic expanding, and slowly rotating sphere, surrounded by vacuum. We find that as the universe expands, the frame dragging weakens at its center; and that at later times inertia at the center completely breaks free of the grip of the universe's rotating matter.</p>https://thesis.library.caltech.edu/id/eprint/1915Dissecting the Gravitational Lens B1608+656: Implications for the Hubble Constant
https://resolver.caltech.edu/CaltechETD:etd-09132007-122424
Authors: {'items': [{'email': 'suyu@mpa-garching.mpg.de', 'id': 'Suyu-Sherry-Hsuan', 'name': {'family': 'Suyu', 'given': 'Sherry Hsuan'}, 'orcid': '0000-0001-5568-6052', 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/MQS2-Y860
Strong gravitational lens systems provide a tool for probing galaxy mass distributions (independent of their light profiles) and for measuring cosmological parameters. In a strong lens system, the background source intensity distribution is multiply imaged. If the source intensity is time varying, then the multiple images of the variable source are delayed in time relative to each other due to the different light travel time along the multiple light paths. One can use lens systems to measure the Hubble constant by obtaining the relative time delays between the multiple images and modeling the lens potential. B1608+656 is a quadruply imaged gravitational lens system with a spatially extended source intensity distribution and two interacting galaxy lenses. This system is unique in that the three relative time delays between the four images were measured accurately with errors of only a few percent, and it thus provides an opportunity to measure the Hubble constant with high precision. The extended source intensity distribution in B1608+656 provides additional constraints on the lens potential, though simultaneous determination of the source intensity and lens potential distribution is needed. The presence of dust and interacting galaxy lenses further complicate this system. We present a comprehensive analysis in a Bayesian framework that takes into account the extended source intensity distribution, interacting galaxy lenses, and the presence of dust for reconstructing the lens potential. Using the deep HST ACS observations on B1608+656, the resulting statistical uncertainty on H_0 associated with the lens modeling is limited by the uncertainty in the best time delay measurement (~3%). The dominant systematic error on H_0 is due to the effects of the environment on B1608+656 (mass-sheet degeneracy). By using the measured velocity dispersion of the lens galaxies and considering the mass structures along the line of sight to B1608+656, we place constraints on the external convergence associated with galaxy groups and mass structure along the line of sight. The resulting Hubble constant from B1608+656 is H_0 = 72 ± 2 (stat.) ± 4 (syst.) km s^-1 Mpc^-1.
https://thesis.library.caltech.edu/id/eprint/3526The Three Ss of Gravitational-Wave Astronomy: Sources, Signals, Searches
https://resolver.caltech.edu/CaltechETD:etd-03112008-012506
Authors: {'items': [{'email': 'Ilya.Mandel@monash.edu', 'id': 'Mandel-Ilya', 'name': {'family': 'Mandel', 'given': 'Ilya'}, 'orcid': '0000-0002-6134-8946', 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/GABY-T236
As gravitational wave astronomy prepares for the first detections of gravitational waves from compact-object binary inspirals, theoretical work is required on the study of (i) gravitational-wave sources, (ii) the signals emitted by those sources, and (iii) the searches for those signals in detector data. This thesis describes work on all three fronts. (i) We discuss intermediate-mass-ratio inspirals (IMRIs) of black holes or neutron stars into intermediate-mass black holes (IMBHs) that could be detected with Advanced LIGO. We analyze different mechanisms of IMRI formation and compute IMRI event rates of up to tens of events per year for Advanced LIGO. We study the spin evolution of IMBHs that grow through a series of minor mergers. We explore how a deviation of an IMRI's central body from a Kerr black hole influences geodesics, including the possibility of chaotic orbital dynamics. We also address the scientific consequences of extreme-mass-ratio inspiral (EMRI) detections by LISA for astrophysics and general relativity, and the difficulties associated with detecting and analyzing EMRI signals. (ii) We study the periodic standing-wave approximation (PSWA), which can potentially provide accurate waveforms in the last inspiral cycles of a comparable-mass black-hole binary. Using a simple model, we find that the solution to Einstein's equations for inspiraling black holes can be recovered to a high accuracy by the addition a perturbative radiation-reaction field to the standing-wave, noninspiraling solution. (iii) We demonstrate the utility of searching for and analyzing tracks in time-frequency spectrograms of a gravitational-wave signal as a means of estimating the parameters of a massive black-hole binary inspiral, as observed by LISA.https://thesis.library.caltech.edu/id/eprint/926Topics in Gravitational-Wave Physics
https://resolver.caltech.edu/CaltechTHESIS:07152021-205059459
Authors: {'items': [{'id': 'Savov-Pavlin', 'name': {'family': 'Savov', 'given': 'Pavlin'}, 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/72z7-n083
<p>While the astrophysics community is on the brink of detecting the first gravitational-wave signal [1, 2, 3], efforts continue to improve the existing detectors and develop new technologies for future-generation detectors. In parallel, the need is rapidly growing for improved analyzes and interpretations of the science data that comes from the detectors. This thesis contributes to these issues with research results related to (i) the design of possible upgrades for the Advanced detectors for the ground-based Laser Interferometer Gravitational-wave Observatory (AdvLIGO) [4, 5, 6, 7] (i.e. for improved versions of the initial LIGO detectors [9, 10]), and (ii) future data analysis techniques for the Laser Interferometer Space Antenna (LISA) [11, 12] (a planned space-based gravitational-wave mission). More specifically:</p>
<p>Currently, an international array of first-generation ground-based, laser-interferometer gravitational-wave detectors (consisting of LIGO, VIRGO [13, 14], GEO600 [15, 16] and TAMA300 [17]) is actively searching for gravitational waves in the frequency band (10 Hz { 10 kHz), with peak sensitivity at a few hundred Hertz. On September the 30th, 2007, the initial LIGO interferometers finished their Science Run 5 (S5) [18], which collected one year of triple coincidence data at the interferometers' design sensitivity. The next version of LIGO's interferometers, called Enhanced LIGO [19], with amplitude sensitivity improved by a factor about 2 (event rate increased by a factor 2³≃10), is being implemented and will
collect data in science mode in 2009-10. Advanced LIGO is expected to begin operations around 2013. At the end of commissioning, it will have a factor ten better amplitude sensitivity than initial LIGO, which translates to a thousand-fold increase in event rate. Therefore, just a few hours of observations by AdvLIGO will be worth the entire lifetime of initial LIGO. Another significant advantage of the Advanced LIGO design is that it will allow tuning of the sensitivity as a function of frequency, so as to optimize searches for specific astrophysical sources with specific expected spectra.</p>
<p>LISA, the first system of space-based gravitational-wave interferometers, is planned for launch and science operation in 2018 or perhaps somewhat later, depending on political developments. It will operate with peak sensitivity around a few milliHertz and should detect galore of signals simultaneously. The lifetime of the mission is expected to be around five years.</p>
<p>This thesis consists of four chapters: this introductory chapter, two chapters (2 and 3) dealing with research relevant to the technology for a possible upgrade of Advanced LIGO, and one chapter (4) relevant to data analysis for LISA. Specifically: Chapter 2 elucidates the influence of the shape (power profile) of an interferometer's arm-cavity light beams on a tilt instability, in which the tilt of an arm cavity mirror is driven by light pressure. Chapter 3 proves a duality relation between arm cavities with almost at mirrors (as originally planned for AdvLIGO) and cavities with almost concentric spherical mirrors (a design change that has been made, to control the tilt instability). I discovered and used this duality relation numerically in the research reported in Chapter 2, but only later, in collaboration with others, did I prove the duality relation analytically (Chapter 3). Chapter 4 reports details of and results from a Mock LISA Data Challenge in which gravitational wave signals from
(mock) supermassive black-hole binaries were sought and found in simulated LISA data.</p>https://thesis.library.caltech.edu/id/eprint/14305Accurate Gravitational Waveforms from Binary Black-hole Systems
https://resolver.caltech.edu/CaltechETD:etd-01122009-143851
Authors: {'items': [{'email': 'michael.oliver.boyle@gmail.com', 'id': 'Boyle-Michael', 'name': {'family': 'Boyle', 'given': 'Michael'}, 'orcid': '0000-0002-5075-5116', 'show_email': 'YES'}]}
Year: 2009
DOI: 10.7907/7NSM-RW43
<p>We examine various topics involved in the creation of accurate theoretical gravitational waveforms from binary black-hole systems.</p>
<p>In Chapter 2 a pseudospectral numerical code is applied to a set of analytic or near-analytic solutions to Einstein's equations which comprise a testbed for numerical-relativity codes. We then discuss methods for extracting gravitational-wave data from numerical simulations of black-hole binary systems, and introduce a practical technique for obtaining the asymptotic form of that data from finite simulation domains in Chapter 3. A formula is also developed to estimate the size of near-field effects from a compact binary. In Chapter 4 the extrapolated data is then compared to post-Newtonian (PN) approximations. We compare the phase and amplitude of the numerical waveform to a collection of Taylor approximants, cross-validating the numerical and PN waveforms, and investigating the regime of validity of the PN waveforms. Chapter 5 extends that comparison to include Padé and effective-one-body models, and investigates components of the PN models. In each case, a careful accounting is made of errors. Finally, we construct a long post-Newtonian–numerical hybrid waveform and evaluate the performance of LIGO's current data-analysis methods with it. We suggest certain optimizations of those methods, including extending the range of template mass ratios to unphysical ranges for certain values of the total mass, and a simple analytic cutoff frequency for the templates which results in nearly optimal matches for both Initial and Advanced LIGO.</p>
https://thesis.library.caltech.edu/id/eprint/143Topics in Theoretical Astrophysics
https://resolver.caltech.edu/CaltechETD:etd-10142008-155140
Authors: {'items': [{'email': 'chaosli_8@hotmail.com', 'id': 'Li-Chao', 'name': {'family': 'Li', 'given': 'Chao'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/CWB8-VF13
This thesis presents a study of various interesting problems in theoretical astrophysics, including gravitational wave astronomy, gamma ray bursts and cosmology. Chapters 2, 3 and 4 explore prospects for detecting gravitational waves from stellar-mass compact objects spiraling into intermediate-mass black holes with ground-based observatories. It is shown in chapter 2 that if the central body is not a BH but its metric is stationary, axisymmetric, reflection symmetric and asymptotically flat, then the waves will likely be triperiodic, as for a BH. Chapters 3 and 4 show that the evolutions of the waves' three fundamental frequencies and of the complex amplitudes of their spectral components encode (in principle) details of the central body's metric, the energy and angular momentum exchange between the central body and the orbit, and the time-evolving orbital elements. Chapter 5 studies a local readout method to enhance the low frequency sensitivity of detuned signal-recycling interferometers. We provide both the results of improvement in quantum noise and the implementation details in Advanced LIGO. Chapter 6 applies and generalizes causal Wiener filter to data analysis in macroscopic quantum mechanical experiments. With the causal Wiener filter method, we demonstrate that in theory we can put the test masses in the interferometer to its quantum mechanical ground states. Chapter 7 presents some analytical solutions for expanding fireballs, the common theoretical model for gamma ray bursts and soft gamma ray repeaters. We apply our results to SGR 1806-20 and rediscover the mismatch between the model and the afterglow observations. Chapter 8 discusses the reconstruction of the scalar-field potential of the dark energy. We advocate direct reconstruction of the scalar field potential as a way to minimize prior assumptions on the shape, and thus minimize the introduction of bias in the derived potential. Chapter 9 discusses gravitational lensing modifications to cosmic microwave background anisotropies and polarization, produced by a stochastic background of primordial gravitational waves between us and the last scattering surface. Chapter 10 calculates the non-Gaussian covariance of CMB B-modes of polarization.
https://thesis.library.caltech.edu/id/eprint/4090