Horizon symmetries and hairy black holes in AdS
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Springer
Received: July 22, 2020 Accepted: August 18, 2020 Published: September 17, 2020
Horizon symmetries and hairy black holes in AdS
a
Institute for Theoretical Physics, Technische Universit¨ at Wien, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, Austria b Physics Department, University of Buenos Aires FCEyN-UBA and IFIBA-CONICET, Ciudad Universitaria, pabell´ on 1, 1428, Buenos Aires, Argentina c Departamento de F´ısica, Universidad de Concepci´ on, Casilla, 160-C, Concepci´ on, Chile
E-mail: [email protected], [email protected], [email protected] Abstract: We investigate whether supertranslation symmetry may appear in a scenario that involves black holes in AdS space. The framework we consider is massive 3D gravity, which admits a rich black hole phase space, including stationary AdS black holes with softly decaying hair. We consider a set of asymptotic conditions that permits such decaying near the boundary, and which, in addition to the local conformal symmetry, is preserved by an extra local current. The corresponding algebra of diffeomorphisms consists of two copies of Virasoro algebra in semi-direct sum with an infinite-dimensional Abelian ideal. We then reorient the analysis to the near horizon region, where infinite-dimensional symmetries also appear. The supertranslation symmetry at the horizon yields an infinite set of non-trivial charges, which we explicitly compute. The zero-mode of these charges correctly reproduces the black hole entropy. In contrast to Einstein gravity, in the higher-derivative theory subleading terms in the near horizon expansion contribute to the near horizon charges. Such terms happen to capture the higher-curvature corrections to the Bekenstein area law. Keywords: Black Holes, Classical Theories of Gravity ArXiv ePrint: 2007.08422
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)120
JHEP09(2020)120
Laura Donnay,a Gaston Giribetb and Julio Olivac
Contents 1
2 Massive 3D gravity
3
3 Special point
4
4 Hairy black holes in AdS
4
5 Asymptotic symmetries at the boundary
7
6 Horizon symmetries
10
7 Adding rotation: stationary hairy black holes
13
8 Adding the Chern-Simons gravitational term
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9 Conclusions
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A Charge computation
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B BTZ black holes
17
1
Introduction
In the recent years, the Bondi-Metzner-Sachs (BMS) symmetry [1–3], which generates the asymptotic isometries of Minkowski spacetime at null-infinity, has been revisited [4–6] and its relevance to field theory has been reconsidered from a modern perspective. This infinitedimensional symmetry has been found to be relevant in the study of scattering amplitudes of both gravitational and gauge theories in asymptotically Minkowski spacetimes [7], and its connection to the Weinberg soft theorems and to the memory effects led to a new way of studying processes in flat space [8–10]; see [7] and references therein and thereof. More recently, infinite-dimensional symmetries like BMS have also appeared in other geometrical setups, such as
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