A
bstract
It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass
M
, momentum
P
→
, angular momentum
J
→
and boost charge
K
→
, an ...infinite head of supertranslation hair. The distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with super-translation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. A leading-order Bondi-gauge expression is derived for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.
Black hole entropy and soft hair Haco, Sasha; Hawking, Stephen W.; Perry, Malcolm J. ...
The journal of high energy physics,
12/2018, Letnik:
2018, Številka:
12
Journal Article
Recenzirano
Odprti dostop
A
bstract
A set of infinitesimal Virasoro
L
⊗ Virasoro
R
diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space ...formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of ‘Wald-Zoupas’ counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges
c
L
=
c
R
= 12
J
. Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.
The nature of space and time Hawking, Stephen; Penrose, Roger
2010., 20100208, 2010, 1996, 1996-01-01, Letnik:
40
eBook
Who doesn’t love a good argument? When physics heavyweights Stephen W. Hawking and Roger Penrose delivered three sets of back-and-forth lectures capped by a final debate at Cambridge’s Isaac Newton ...Institute, the course of modern cosmological thinking was at stake. As it happens, The Nature of Space and Time, which collects these remarks, suggests that little has changed from the days when Einstein challenged Bohr by refusing to believe that God plays dice. The math is more abstruse, the arguments more refined, but the argument still hinges on whether our physical theories should be expected to model reality or merely predict measurements.
The conformal BMS group Haco, Sasha J.; Hawking, Stephen W.; Perry, Malcolm J. ...
The journal of high energy physics,
11/2017, Letnik:
2017, Številka:
11
Journal Article
Recenzirano
Odprti dostop
A
bstract
We describe the conformal symmetries of asymptotically flat spacetime. These represent an extension of the BMS group that we call the
conformal BMS group
. Its general features are ...discussed.
Soft Hair on Black Holes Hawking, Stephen W; Perry, Malcolm J; Strominger, Andrew
Physical review letters,
2016-Jun-10, Letnik:
116, Številka:
23
Journal Article
Recenzirano
Odprti dostop
It has recently been shown that Bondi-van der Burg-Metzner-Sachs supertranslation symmetries imply an infinite number of conservation laws for all gravitational theories in asymptotically Minkowskian ...spacetimes. These laws require black holes to carry a large amount of soft (i.e., zero-energy) supertranslation hair. The presence of a Maxwell field similarly implies soft electric hair. This Letter gives an explicit description of soft hair in terms of soft gravitons or photons on the black hole horizon, and shows that complete information about their quantum state is stored on a holographic plate at the future boundary of the horizon. Charge conservation is used to give an infinite number of exact relations between the evaporation products of black holes which have different soft hair but are otherwise identical. It is further argued that soft hair which is spatially localized to much less than a Planck length cannot be excited in a physically realizable process, giving an effective number of soft degrees of freedom proportional to the horizon area in Planck units.
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.
First published in 1973, this influential work discusses Einstein's General Theory of Relativity, exploring its predictions relating to black holes and singularities in space-time. A Foreword ...contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context given the subsequent developments in the field.
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