[
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{
"id": "Echeverria-F",
"name": {
"family": "Echeverria",
"given": "Fernando"
}
},
{
"id": "Klinkhammer-G",
"name": {
"family": "Klinkhammer",
"given": "Gunnar"
}
},
{
"id": "Thorne-K-S",
"name": {
"family": "Thorne",
"given": "Kip S."
}
}
]
},
"title": "Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory",
"ispublished": "pub",
"full_text_status": "public",
"keywords": "WEAK ENERGY CONDITION; MACHINES",
"note": "\u00a91991 The American Physical Society. \n\nReceived 27 February 1991. \n\nWe thank Joseph Polchinski for motivating this research by asking, in a letter to one of us, how the laws of physics could deal with paradoxical situations of the sort embodied in Fig. 3(a). For helpful discussions we thank John Friedman, Mike Morris, Nicolas Papastamatiou, Leonard Parker, and Ulvi Yurtsever. This paper was supported in part by National Science Foundation Grant No. AST-8817792.",
"abstract": "The effects of self-interaction in classical physics, in the presence of closed timelike curves, are probed by means of a simple model problem: The motion and self-collisions of a nonrelativistic, classical billiard ball in a space endowed with a wormhole that takes the ball backward in time. The central question asked is whether the Cauchy problem is well posed for this model problem, in the following sense: We define the multiplicity of an initial trajectory for the ball to be the number of self-consistent solutions of the ball's equations of motion, which begin with that trajectory. For the Cauchy problem to be well posed, all initial trajectories must have multiplicity one.\n\nA simple analog of the science-fiction scenario of going back in time and killing oneself is an initial trajectory which is dangerous in this sense: When followed assuming no collisions, the trajectory takes the ball through the wormhole and thereby back in time, and then sends the ball into collision with itself. In contrast with one's naive expectation that dangerous trajectories might have multiplicity zero and thereby make the Cauchy problem ill posed (\"no solutions\"), it is shown that all dangerous initial trajectories in a wide class have infinite multiplicity and thereby make the Cauchy problem ill posed in an unexpected way: \"far too many solutions.\"\n\nThe wide class of infinite-multiplicity, dangerous trajectories includes all those that are nearly coplanar with the line of centers between the wormhole mouths, and a ball and wormhole restricted by (ball radius)\u226a(wormhole radius)\u226a(separation between wormhole mouths). Two of the infinity of solutions are slight perturbations of the self-inconsistent, collision-free motion, and all the others are strongly different from it. Not all initial trajectories have infinite multiplicity: trajectories where the ball is initially at rest far from the wormhole have multiplicity one, as also, probably, do those where it is almost at rest. A search is made for initial trajectories with zero multiplicity, and none are found. The search entails constructing a set of highly nonlinear, coupled, algebraic equations that embody all the ball's laws of motion, collision, and wormhole traversal, and then constructing perturbation theory and numerical solutions of the equations. A future paper (paper II) will show that, when one takes account of the effects of quantum mechanics, the classically ill-posed Cauchy problem (\"too many classical solutions\") becomes quantum-mechanically well posed in the sense of producing unique probability distributions for the outcomes of all measurements.",
"date": "1991-08-15",
"date_type": "published",
"publication": "Physical Review D",
"volume": "44",
"number": "4",
"publisher": "Physical Review D",
"pagerange": "1077-1099",
"id_number": "CaltechAUTHORS:ECHprd91",
"issn": "2470-0010",
"official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ECHprd91",
"rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.",
"local_group": {
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}
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},
"doi": "10.1103/PhysRevD.44.1077",
"primary_object": {
"basename": "ECHprd91.pdf",
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"resource_type": "article",
"pub_year": "1991",
"author_list": "Echeverria, Fernando; Klinkhammer, Gunnar; et el."
},
{
"id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/aw0a8-ps286",
"eprint_id": 3737,
"eprint_status": "archive",
"datestamp": "2023-08-22 07:45:05",
"lastmod": "2023-10-16 16:08:13",
"type": "article",
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"creators": {
"items": [
{
"id": "Friedman-J",
"name": {
"family": "Friedman",
"given": "John"
}
},
{
"id": "Morris-M-S",
"name": {
"family": "Morris",
"given": "Michael S."
}
},
{
"id": "Novikov-I-D",
"name": {
"family": "Novikov",
"given": "Igor D."
}
},
{
"id": "Echeverria-F",
"name": {
"family": "Echeverria",
"given": "Fernando"
}
},
{
"id": "Klinkhammer-G",
"name": {
"family": "Klinkhammer",
"given": "Gunnar"
}
},
{
"id": "Thorne-K-S",
"name": {
"family": "Thorne",
"given": "Kip S."
}
},
{
"id": "Yurtsever-U",
"name": {
"family": "Yurtsever",
"given": "Ulvi"
}
}
]
},
"title": "Cauchy problem in spacetimes with closed timelike curves",
"ispublished": "pub",
"full_text_status": "public",
"note": "\u00a91990 The American Physical Society. \n\nReceived 5 June 1990. \n\nFor helpful discussions with one or another of us we thank Arley Anderson, Valery Frolov, Robert Geroch, Jonathan Halliwell, William Hiscock, James Hartle, Leonard Parker, Joe Polchinski, Carl Sagan, Edwin Salpeter, and Robert Wald. This research was supported in part by the National Science Foundation (Grants Nos. PHY-8603173 at the University of Wisconsin, and AST-8514911 and AST-8817792 at Caltech), by the Academy of Sciences of the USSR, and by the International Center for Theoretical Physics at Trieste.",
"abstract": "The laws of physics might permit the existence, in the real Universe, of closed timelike curves (CTC's). Macroscopic CTC's might be a semiclassical consequence of Planck-scale, quantum gravitational, Lorentzian foam, if such foam exists. If CTC's are permitted, then the semiclassical laws of physics (the laws with gravity classical and other fields quantized or classical) should be augmented by a principle of self-consistency, which states that a local solution to the equations of physics can occur in the real Universe only if it can be extended to be part of a global solution, one which is well defined throughout the (nonsingular regions of) classical spacetime. The consequences of this principle are explored for the Cauchy problem of the evolution of a classical, massless scalar field \u03a6 (satisfying \u25a1\u03a6=0) in several model spacetimes with CTC's.\n\nIn general, self-consistency constrains the initial data for the field \u03a6. For a family of spacetimes with traversible wormholes, which initially possess no CTC's and then evolve them to the future of a stable Cauchy horizon scrH, self-consistency seems to place no constraints on initial data for \u03a6 that are posed on past null infinity, and none on data posed on spacelike slices which precede scrH.\n\nBy contrast, initial data posed in the future of scrH, where the CTC's reside, are constrained; but the constraints appear to be mild in the sense that in some neighborhood of every event one is free to specify initial data arbitrarily, with the initial data elsewhere being adjusted to guarantee self-consistent evolution. A spacetime whose self-consistency constraints have this property is defined to be ''benign with respect to the scalar field \u03a6.'' The question is posed as to whether benign spacetimes in some sense form a generic subset of all spacetimes with CTC's. It is shown that in the set of flat, spatially and temporally closed, 2-dimensional spacetimes the benign ones are not generic. However, it seems likely that every 4-dimensional, asymptotically flat space-time that is stable and has a topology of the form R\u00d7(S-one point), where S is a closed 3-manifold, is benign. Wormhole spacetimes are of this type, with S=S^1\u00d7S^2. We suspect that these types of self-consistency behavior of the scalar field \u03a6 are typical for noninteracting (linearly superposing), classical fields.\n\nHowever, interacting classical systems can behave quite differently, as is demonstrated by a study of the motion of a hard-sphere billiard ball in a wormhole spacetime with closed timelike curves: If the ball is classical, then some choices of initial data (some values of the ball's initial position and velocity) give rise to unique, self-consistent motions of the ball; other choices produce two different self-consistent motions; and others might (but we are not yet sure) produce no self-consistent motions whatsoever. By contrast, in a path-integral formulation of the nonrelativistic quantum mechanics of such a billiard ball, there appears to be a unique, self-consistent set of probabilities for the outcomes of all measurements. This paper's conclusion, that CTC's may not be as nasty as people have assumed, is reinforced by the fact that they do not affect Gauss's theorem and thus do not affect the derivation of global conservation laws from differential ones. The standard conservation laws remain valid globally, and in asymptotically flat, wormhole spacetimes they retain a natural, quasilocal interpretation.",
"date": "1990-09-15",
"date_type": "published",
"publication": "Physical Review D",
"volume": "42",
"number": "6",
"publisher": "Physical Review D",
"pagerange": "1915-1930",
"id_number": "CaltechAUTHORS:FRIprd90",
"issn": "2470-0010",
"official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FRIprd90",
"rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.",
"local_group": {
"items": [
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}
]
},
"doi": "10.1103/PhysRevD.42.1915",
"primary_object": {
"basename": "FRIprd90.pdf",
"url": "https://authors.library.caltech.edu/records/aw0a8-ps286/files/FRIprd90.pdf"
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"resource_type": "article",
"pub_year": "1990",
"author_list": "Friedman, John; Morris, Michael S.; et el."
},
{
"id": "https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tkfxw-43s17",
"eprint_id": 6540,
"eprint_status": "archive",
"datestamp": "2023-08-22 06:57:38",
"lastmod": "2023-10-16 20:23:25",
"type": "article",
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"creators": {
"items": [
{
"id": "Echeverria-F",
"name": {
"family": "Echeverria",
"given": "Fernando"
}
}
]
},
"title": "Gravitational-wave measurements of the mass and angular momentum of a black hole",
"ispublished": "pub",
"full_text_status": "public",
"note": "\u00a91989 The American Physical Society \n\nReceived 27 December 1988 \n\nI wish to thank Dr. Kip S. Thorne, for suggesting this problem to me and for many suggestions that helped me with the research and in writing this paper. I am also indebted to Dr. E.W. Leaver, who supplied me with his unpublished numerical results on the frequencies and damping times of the fundamental l = m = 2 mode of Kerr black holes, which were necessary for my calculations. This work was supported in part by the National Science Foundation under Grant No. AST85-14911.",
"abstract": "A deformed black hole produced in a cataclysmic astrophysical event should undergo damped vibrations which emit gravitational radiation. By fitting the observed gravitational waveform h(t) to the waveform predicted for black-hole vibrations, it should be possible to deduce the hole's mass M and dimensionless rotation parameter a=(c/G)(angular momentum)/M^2. This paper estimates the accuracy with which M and a can be determined by optimal signal processing of data from laser-interferometer gravitational-wave detectors. It is assumed that the detector noise has a white spectrum and has been made Gaussian by cross correlation of detectors at different sites. Assuming, also, that only the most slowly damped mode (which has spheroidal harmonic indices l=m=2) is significantly excited\u2014as probably will be the case for a hole formed by the coalescence of a neutron-star binary or a black-hole binary\u2014it is found that the one-sigma uncertainties in M and a are \u0394M/M\u22432.2\u03c1^-1(1-a)^0.45, \u0394a\u22435.9\u03c1^-1(1-a)^1.06, where \u03c1\u2243hs(\u03c0Sh)^-1/2 (1-a)^-0.22. Here \u03c1 is the amplitude signal-to-noise ratio at the output of the optimal filter, hs is the wave's amplitude at the beginning of the vibrations, f is the wave's frequency (the angular frequency \u03c9 divided by 2\u03c0), and Sh is the frequency-independent spectral density of the detectors' noise. These formulas for \u0394M and \u0394a are valid only for \u03c1\u227310. Corrections to these approximate formulas are given in Table II.",
"date": "1989-11-15",
"date_type": "published",
"publication": "Physical Review D",
"volume": "40",
"number": "10",
"publisher": "Physical Review D",
"pagerange": "3194-3203",
"id_number": "CaltechAUTHORS:ECHprd89",
"issn": "2470-0010",
"official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ECHprd89",
"rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.",
"doi": "10.1103/PhysRevD.40.3194",
"primary_object": {
"basename": "ECHprd89.pdf",
"url": "https://authors.library.caltech.edu/records/tkfxw-43s17/files/ECHprd89.pdf"
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"resource_type": "article",
"pub_year": "1989",
"author_list": "Echeverria, Fernando"
}
]