CaltechAUTHORS: Article
https://feeds.library.caltech.edu/people/Franklin-J/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 04 Oct 2024 19:00:59 -0700Shortcuts to spherically symmetric solutions: a cautionary note
https://resolver.caltech.edu/CaltechAUTHORS:20170314-142458757
Year: 2004
DOI: 10.1088/0264-9381/21/22/N01
Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the surviving metric components. This shortcut is not to be overdone; however, a one-function ansatz invalidates it, as illustrated by the incorrect solutions of Wohlfarth (2004 Class. Quantum Grav. 21 1927).https://resolver.caltech.edu/CaltechAUTHORS:20170314-142458757Birkhoff for Lovelock redux
https://resolver.caltech.edu/CaltechAUTHORS:20170314-133214489
Year: 2005
DOI: 10.1088/0264-9381/22/16/L03
We show succinctly that all metric theories with second order field equations obey Birkhoff's theorem: their spherically symmetric solutions are static.https://resolver.caltech.edu/CaltechAUTHORS:20170314-133214489Time (in)dependence in general relativity
https://resolver.caltech.edu/CaltechAUTHORS:20100205-080823285
Year: 2007
DOI: 10.1119/1.2426351
We clarify the conditions for Birkhoff's theorem, that is, time independence in general relativity. We work primarily at the linearized level where guidance from electrodynamics is particularly useful. As a bonus, we also review how the equivalence principle results from general relativity. The basic time-independent solutions due to Schwarzschild and Kerr provide concrete illustrations of the theorem. Only familiarity with Maxwell's equations and tensor analysis is required.https://resolver.caltech.edu/CaltechAUTHORS:20100205-080823285Circular symmetry in topologically massive gravity
https://resolver.caltech.edu/CaltechAUTHORS:20100521-094915260
Year: 2010
DOI: 10.1088/0264-9381/27/10/107002
We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null.https://resolver.caltech.edu/CaltechAUTHORS:20100521-094915260Is BTZ a separate superselection sector of CTMG?
https://resolver.caltech.edu/CaltechAUTHORS:20101209-081925006
Year: 2010
DOI: 10.1016/j.physletb.2010.09.019
We exhibit exact solutions of (positive) matter coupled to original "wrong G-sign" cosmological TMG. They all evolve to conical singularity, rather than to black hole – here negative mass – BTZ. This provides evidence that the latter constitute a separate "superselection" sector, one that unlike in GR, is not reachable by physical sources.https://resolver.caltech.edu/CaltechAUTHORS:20101209-081925006De/re-constructing the Kerr metric
https://resolver.caltech.edu/CaltechAUTHORS:20101109-081445939
Year: 2010
DOI: 10.1007/s10714-010-1002-8
We derive the Kerr solution in a pedagogically transparent way, using physical symmetry and gauge arguments to reduce the candidate metric to just two unknowns. The resulting field equations are then easy to obtain, and solve. Separately, we transform the Kerr metric to Schwarzschild frame to exhibit its limits in that familiar setting.https://resolver.caltech.edu/CaltechAUTHORS:20101109-081445939The Bel-Robinson tensor for topologically massive gravity
https://resolver.caltech.edu/CaltechAUTHORS:20110316-093515136
Year: 2011
DOI: 10.1088/0264-9381/28/3/032002
We construct, and establish the (covariant) conservation of, a 4-index 'super stress tensor' for topologically massive gravity. Separately, we discuss its invalidity in quadratic curvature models and suggest a generalization.https://resolver.caltech.edu/CaltechAUTHORS:20110316-093515136No Bel–Robinson tensor for quadratic curvature theories
https://resolver.caltech.edu/CaltechAUTHORS:20120124-082154767
Year: 2011
DOI: 10.1088/0264-9381/28/23/235016
We attempt to generalize the familiar covariantly conserved Bel–Robinson tensor B_(μναβ) ~ RR of GR and its recent topologically massive third derivative order counterpart B ~ RDR to quadratic curvature actions. Two very different models of current interest are examined: fourth-order D = 3 'new massive gravity' and second-order D > 4 Lanczos–Lovelock. On dimensional grounds, the candidates here become B ~ DRDR + RRR. For the D = 3 model, there indeed exist conserved B ~ ∂R∂R in the linearized limit. However, despite a plethora of available cubic terms, B cannot be extended to the full theory. The D > 4 models are not even linearizable about flat space, since their field equations are quadratic in curvature; they also have no viable B, a fact that persists even if one includes cosmological or Einstein terms to allow linearization about the resulting dS vacua. These results are an unexpected, if hardly unique, example of linearization instability.https://resolver.caltech.edu/CaltechAUTHORS:20120124-082154767Canonical analysis and stability of Lanczos–Lovelock gravity
https://resolver.caltech.edu/CaltechAUTHORS:20120420-140700303
Year: 2012
DOI: 10.1088/0264-9381/29/7/072001
We perform a spacetime analysis of the D > 4 quadratic curvature Lanczos–Lovelock (LL) model, exhibiting its dependence on intrinsic/extrinsic curvatures, lapse and shifts. As expected from general covariance, the field equations include D constraints, of zeroth and first time derivative order. In the 'linearized'—here necessarily cubic—limit, we give an explicit formulation in terms of the usual ADM metric decomposition, incidentally showing that time derivatives act only on its transverse-traceless spatial components. Unsurprisingly, pure LL has no Hamiltonian formulation, nor are even its—quadratic—weak-field constraints easily soluble. Separately, we point out that the extended, more physical R + LL model is stable—its energy is positive—due to its supersymmetric origin and ghost-freedom.https://resolver.caltech.edu/CaltechAUTHORS:20120420-140700303Symmetrically reduced Galileon equations and solutions
https://resolver.caltech.edu/CaltechAUTHORS:20120831-142152025
Year: 2012
DOI: 10.1103/PhysRevD.86.047701
The maximally complicated arbitrary-dimensional "maximal" Galileon field equations simplify dramatically for symmetric configurations. Thus, spherical symmetry reduces the equations from the D- to the two-dimensional (Monge-Ampere) equation, axial symmetry to its cubic extension, etc. We can then obtain explicit solutions, such as spherical or axial waves, and relate them to the (known) general, but highly implicit, lower-D solutions.https://resolver.caltech.edu/CaltechAUTHORS:20120831-142152025Bel-Robinson as stress-tensor gradients and their extensions to massive matter
https://resolver.caltech.edu/CaltechAUTHORS:20150316-143151667
Year: 2015
DOI: 10.1007/s10714-015-1909-1
We show that the Bel–Robinson (BR) tensor is—generically, as well as in its original GR setting—an autonomously conserved part of the, manifestly conserved, double gradient of a system's stress-tensor. This suggests its natural extension from GR to matter models, first to (known) massless scalars and vectors, then to massive ones, including tensors. These massive versions are to be expected, given that they arise upon KK reduction of massless D+1D+1 ones. We exhibit the resulting spin (0,1,2)(0,1,2) "massive" BR.https://resolver.caltech.edu/CaltechAUTHORS:20150316-143151667