The Singularities of gravitational collapse and cosmology
Stephen W. Hawking,Roger Penrose +1 more
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In this article, a new theorem on space-time singularities is presented which largely incorporates and generalizes the previously known results and applies if the universe is spatially closed or there is an object undergoing relativistic gravitational collapse (existence of a trapped surface).Abstract:
A new theorem on space-time singularities is presented which largely incorporates and generalizes the previously known results. The theorem implies that space-time singularities are to be expected if either the universe is spatially closed or there is an ‘object’ undergoing relativistic gravitational collapse (existence of a trapped surface) or there is a point p whose past null cone encounters sufficient matter that the divergence of the null rays through p changes sign somewhere to the past of p (i. e. there is a minimum apparent solid angle, as viewed from p for small objects of given size). The theorem applies if the following four physical assumptions are made: (i) Einstein’s equations hold (with zero or negative cosmological constant), (ii) the energy density is nowhere less than minus each principal pressure nor less than minus the sum of the three principal pressures (the ‘energy condition’), (iii) there are no closed timelike curves, (iv) every timelike or null geodesic enters a region where the curvature is not specially alined with the geodesic. (This last condition would hold in any sufficiently general physically realistic model.) In common with earlier results, timelike or null geodesic incompleteness is used here as the indication of the presence of space-time singularities. No assumption concerning existence of a global Cauchy hypersurface is required for the present theorem.read more
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Particle Creation by Black Holes
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.
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Black holes in general relativity
TL;DR: In this paper, it is shown that a stationary black hole must have topologically spherical boundary and must be axisymmetric if it is rotating, and these results together with those of Israel and Carter go most of the way towards establishing the conjecture that any stationary blackhole is a Kerr solution.
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Testing general relativity with present and future astrophysical observations
Emanuele Berti,Emanuele Berti,Enrico Barausse,Vitor Cardoso,Vitor Cardoso,Leonardo Gualtieri,Paolo Pani,Paolo Pani,Ulrich Sperhake,Ulrich Sperhake,Ulrich Sperhake,Leo C. Stein,Leo C. Stein,Norbert Wex,Kent Yagi,Kent Yagi,Tessa Baker,C.P. Burgess,C.P. Burgess,Flávio S. Coelho,Daniela D. Doneva,Antonio De Felice,Pedro G. Ferreira,Paulo C. C. Freire,James Healy,Carlos A. R. Herdeiro,Michael Horbatsch,Burkhard Kleihaus,Antoine Klein,Kostas D. Kokkotas,Jutta Kunz,Pablo Laguna,Ryan N. Lang,Ryan N. Lang,Ryan N. Lang,Tjonnie G. F. Li,Tjonnie G. F. Li,Tyson Littenberg,Andrew Matas,S. Mirshekari,Hirotada Okawa,Eugen Radu,Richard O'Shaughnessy,Richard O'Shaughnessy,Bangalore Suryanarayana Sathyaprakash,Chris Van Den Broeck,Hans A. Winther,Helvi Witek,Mir Emad Aghili,Justin Alsing,Brett Bolen,Luca Bombelli,Sarah Caudill,Liang Chen,Juan Carlos Degollado,Ryuichi Fujita,Caixia Gao,Davide Gerosa,Saeed Kamali,Hector O. Silva,João G. Rosa,Laleh Sadeghian,Marco O. P. Sampaio,Hajime Sotani,Miguel Zilhão +64 more
TL;DR: In this article, a catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory is presented, and the current understanding of the structure and dynamics of compact objects in these theories is summarized.
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The inverse mean curvature flow and the Riemannian Penrose Inequality
Gerhard Huisken,Tom Ilmanen +1 more
TL;DR: In this article, a theory of weak solutions of the inverse mean curvature flow was developed and employed to prove the Riemannian Penrose inequality for each connected component of a 3-manifold of nonnegative scalar curvature.
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Formation and Evaporation of Nonsingular Black Holes
TL;DR: Regular (nonsingular) space-times are given that describe the formation of a (locally defined) black hole from an initial vacuum region, its quiescence as a static region, and its subsequent evaporation to a vacuum region.
References
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Mach's principle and a relativistic theory of gravitation
Carl H. Brans,R. H. Dicke +1 more
TL;DR: In this paper, the role of Mach's principle in physics is discussed in relation to the equivalence principle and the difficulties encountered in attempting to incorporate Mach's principles into general relativity are discussed.
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Mach's Principle and Invariance under Transformation of Units
TL;DR: In this article, it is shown that a coordinate-dependent transformation of the units of measure can be used to throw the theory into a form for which the gravitational field appears in the conventional form, as a metric tensor, such that the Einstein field equation is satisfied.
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Spinor structure of space-times in general relativity. i
TL;DR: In this paper, it is proved that a necessary and sufficient condition for a non-compact space-time M to admit a spinor structure is that M have a global field of orthonormal tetrads.