Diffeomorphism on the horizon as an asymptotic isometry of the Schwarzschild black hole

Hotta, Masahiro; Sasaki, Kazuo; Sasaki, Takayoshi

doi:10.1088/0264-9381/18/10/301

Cited by 56 publications

(81 citation statements)

References 13 publications

(25 reference statements)

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“…, and the Poisson bracket algebra of the conserved charges is given by 23) such that H ′ [ 0 g; ζ] = 0, the Poisson bracket algebra becomes 24) where the central term has been eliminated, in contrast to the Virasoro algebra Eq. (1.2) in the case of the 3-d anti-de Sitter spacetime [8].…”

Section: Poisson Bracket Algebra Of the Asymptotic Symmetriesmentioning

confidence: 99%

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Asymptotic symmetries on Killing horizons

Koga

2001

Phys. Rev. D

134

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We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in the Einstein theory with or without the cosmological constant. Those asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of asymptotic Killing vectors and find that the group of the asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved under not only diffeomorphisms but also non-trivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff (S 1 ) subgroup, which results from the supertranslations dependent only on the null coordinate, it is shown that the Poisson bracket algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire non-trivial central charges. Finally, by considering extended symmetries, we discuss that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with non-trivial central charges, which will not be justified when we respect the spherical symmetry of Killing horizons.

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Section: Poisson Bracket Algebra Of the Asymptotic Symmetriesmentioning

confidence: 99%

“…Particularly, the conserved charges in the case of ω = ω(θ, φ) have been analyzed in Ref. [23], where it is claimed that the algebra of the conserved charges does not involve any anomalous terms like a central charge.…”

Section: Extended Symmetriesmentioning

confidence: 99%

Asymptotic symmetries on Killing horizons

Koga

2001

Phys. Rev. D

134

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“…We thank Gerardo Adesso and Bartosz Regula for a helpful discussion on entanglement monotones and Masahiro Hotta for bringing the work in [5,6] where Q ϵ has the property that Q ϵ → 1 as ϵ → 0. The first equality in (A.2) follows from formula 6.576.4 in [28], and the second equality follows using standard properties of the Gamma-function [25].…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…Such degrees of freedom exist already in Minkowski spacetime electrodynamics [4], and in the gravitational case these degrees of freedom are associated with supertranslations in the BondiMetzner-Sachs (BMS) group of asymptotic isometries at the infinity [5][6][7][8][9][10]. Contributions to the ongoing debate include [11,12].…”

Section: Introductionmentioning

confidence: 99%

Quantum memory for Rindler supertranslations

Kolekar

Louko

2018

Phys. Rev. D

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The Rindler horizon in Minkowski spacetime can be implanted with supertranslation hair by a matter shock wave without planar symmetry, and the hair is observable as a supertranslation memory on the Rindler family of uniformly linearly accelerated observers. We show that this classical memory is accompanied by a supertranslation quantum memory that modulates the entanglement between the opposing Rindler wedges in quantum field theory. A corresponding phenomenon across a black hole horizon may play a role in Hawking, Perry, and Strominger's proposal for supertranslations to provide a solution to the black hole information paradox.

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“…These diffeomorphisms preserve the form (38) of the metric. Horizon supertranslations have been studied from a variety of viewpoints in [25,[61][62][63]. Some of these authors allow f to depend on v.…”

Section: Prl 116 231301 (2016) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Black Holes Have Soft Quantum Hair

Horowitz

2016

Physics

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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.

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Diffeomorphism on the horizon as an asymptotic isometry of the Schwarzschild black hole

Cited by 56 publications

References 13 publications

Asymptotic symmetries on Killing horizons

Asymptotic symmetries on Killing horizons

Quantum memory for Rindler supertranslations

Black Holes Have Soft Quantum Hair

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