The question of cosmic censorship
TL;DR: Cosmic censorship is discussed in this paper in various facets and it is concluded that rather little clear-cut progress has been made to date, and that the question is still very much open.
Abstract: Cosmic censorship is discussed in its various facets. It is concluded that rather little clear-cut progress has been made to date, and that the question is still very much open.
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01 Dec 1982
TL;DR: In this paper, the authors study the solutions of the gravitational field equations which describe the contraction of a heavy star, and give general and qualitative arguments on the behavior of the metrical tensor as the contraction progresses.
Abstract: When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.
1,052 citations
TL;DR: In this paper, the authors provide a review of various types of black hole remnants, and provide some new thoughts regarding the challenges that black hole survivors face in the context of the information loss paradox and its latest incarnation, namely the firewall controversy.
287 citations
TL;DR: In this paper, the area of a marginally trapped surface formed by a head-on collision of gravitational shock waves in AdS{sub D} was calculated and a lower bound on the entropy produced after the collision was derived.
Abstract: We calculate the area of a marginally trapped surface formed by a head-on collision of gravitational shock waves in AdS{sub D}. We use this to obtain a lower bound on the entropy produced after the collision. A comparison to entropy production in heavy-ion collisions is included. We also discuss an O(D-2) remnant of conformal symmetry, which is present in a class of gravitational shockwave collisions in AdS{sub D} and which might be approximately realized (with D=5) in central heavy-ion collisions.
225 citations
TL;DR: It is shown that if instead the black hole starts out with below maximal spin, then indeed overspinning can be achieved and requirements on the size and internal structure of the test body can be met.
Abstract: It has long been known that a maximally spinning black hole cannot be overspun by tossing in a test body. Here we show that if instead the black hole starts out with below maximal spin, then indeed overspinning can be achieved. We find that requirements on the size and internal structure of the test body can be met if the body carries in orbital but not spin angular momentum. Our analysis neglects radiative and self-force effects, which may prevent the overspinning.
224 citations
TL;DR: In this article, a general, unified, and rigorous analytical framework for using gravitational lensing by compact objects to test different theories of gravity beyond the weak-deflection limit was developed.
Abstract: We are developing a general, unified, and rigorous analytical framework for using gravitational lensing by compact objects to test different theories of gravity beyond the weak-deflection limit. In this paper we present the formalism for computing corrections to lensing observables for static, spherically symmetric gravity theories in which the corrections to the weak-deflection limit can be expanded as a Taylor series in one parameter, namely, the gravitational radius of the lens object. We take care to derive coordinate-independent expressions and compute quantities that are directly observable. We compute series expansions for the observables that are accurate to second order in the ratio $\ensuremath{\epsilon}={\ensuremath{\vartheta}}_{\ifmmode\bullet\else\textbullet\fi{}}/{\ensuremath{\vartheta}}_{E}$ of the angle subtended by the lens's gravitational radius to the weak-deflection Einstein radius, which scales with mass as $\ensuremath{\epsilon}\ensuremath{\propto}{M}_{\ifmmode\bullet\else\textbullet\fi{}}^{1/2}$. The positions, magnifications, and time delays of the individual images have corrections at both first and second order in $\ensuremath{\epsilon}$, as does the differential time delay between the two images. Interestingly, we find that the first-order corrections to the total magnification and centroid position vanish in all gravity theories that agree with general relativity in the weak-deflection limit, but they can remain nonzero in modified theories that disagree with general relativity in the weak-deflection limit. For the Reissner-Nordstr\"om metric and a related metric from heterotic string theory, our formalism reveals an intriguing connection between lensing observables and the condition for having a naked singularity, which could provide an observational method for testing the existence of such objects. We apply our formalism to the galactic black hole and predict that the corrections to the image positions are at the level of $10\text{ }\text{ }\ensuremath{\mu}\mathrm{arc}\text{ }\mathrm{s}$ (microarcseconds), while the correction to the time delay is a few hundredths of a second. These corrections would be measurable today if a pulsar were found to be lensed by the galactic black hole, and they should be readily detectable with planned missions like MAXIM.
194 citations
References
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TL;DR: In this article, it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature, which leads to a slow decrease in the mass of the black hole and to its eventual disappearance.
Abstract: In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.
10,923 citations
Book•
01 Jan 1973
TL;DR: In this paper, the authors discuss the General Theory of Relativity in the large and discuss the significance of space-time curvature and the global properties of a number of exact solutions of Einstein's field equations.
Abstract: Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
8,932 citations
Book•
01 Jan 1984
TL;DR: The calculus of 2-spinors was introduced and systematically developed in this article, which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations.
Abstract: This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.
2,260 citations
01 Mar 2010
TL;DR: In this paper, Weinberg et al. present a survey of the history of the field of quantum physics and its application to the theory of the Kerr metric and its peturbations.
Abstract: List of contributors Preface 1. An introductory survey S. W. Hawking and W. Israel 2. The confrontation between gravitation theory and experiment C. M. Will 3. Gravitational-radiation experiments D. H. Douglass and V. B. Braginsky 4. The initial value problem and the dynamical formulation of general relativity A. E. Fischer and J. E. Marsden 5. Global structure of spacetimes R. Geroch and G. T. Horowitz 6. The general theory of the mechanical, electromagnetic and thermodynamic properties of black holes B. Carter 7. An introduction to the theory of the Kerr metric and its peturbations S. Chandrasekhar 8. Black hole astrophysics R. D. Blandford and K. S. Thorne 9. The big bang cosmology - enigmas and nostrums R. H. Dicke and P. J. E. Peebles 10. Cosmology and the early universe Ya B. Zel'dovitch 11. Anisotropic and inhomogeneous relativistic cosmologies M. A. H. MacCallum 12. Singularities and time-asymmetry R. Penrose 13. Quantum field theory in curved spacetime G. W. Gibbons 14. Quantum gravity: the new synthesis B. S. DeWitt 15. The path-integral approach to quantum gravity S. W. Hawking 16. Ultraviolet divergences in quantum theories of gravitation S. Weinberg References Index.
1,911 citations
Book•
16 Aug 1979
TL;DR: In this article, Weinberg et al. present a survey of the history of the field of quantum physics and its application to the theory of the Kerr metric and its peturbations.
Abstract: List of contributors Preface 1. An introductory survey S. W. Hawking and W. Israel 2. The confrontation between gravitation theory and experiment C. M. Will 3. Gravitational-radiation experiments D. H. Douglass and V. B. Braginsky 4. The initial value problem and the dynamical formulation of general relativity A. E. Fischer and J. E. Marsden 5. Global structure of spacetimes R. Geroch and G. T. Horowitz 6. The general theory of the mechanical, electromagnetic and thermodynamic properties of black holes B. Carter 7. An introduction to the theory of the Kerr metric and its peturbations S. Chandrasekhar 8. Black hole astrophysics R. D. Blandford and K. S. Thorne 9. The big bang cosmology - enigmas and nostrums R. H. Dicke and P. J. E. Peebles 10. Cosmology and the early universe Ya B. Zel'dovitch 11. Anisotropic and inhomogeneous relativistic cosmologies M. A. H. MacCallum 12. Singularities and time-asymmetry R. Penrose 13. Quantum field theory in curved spacetime G. W. Gibbons 14. Quantum gravity: the new synthesis B. S. DeWitt 15. The path-integral approach to quantum gravity S. W. Hawking 16. Ultraviolet divergences in quantum theories of gravitation S. Weinberg References Index.
1,806 citations