Extended symmetries at the black hole horizon

We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to...

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Publicado:	2016
Materias:	Black Holes Gauge Symmetry Space-Time Symmetries
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11266708_v2016_n9_p_Donnay http://hdl.handle.net/20.500.12110/paper_11266708_v2016_n9_p_Donnay
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_11266708_v2016_n9_p_Donnay
record_format	dspace
spelling	paper:paper_11266708_v2016_n9_p_Donnay2023-06-08T16:08:48Z Extended symmetries at the black hole horizon Black Holes Gauge Symmetry Space-Time Symmetries We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Witt algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature. © 2016, The Author(s). 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11266708_v2016_n9_p_Donnay http://hdl.handle.net/20.500.12110/paper_11266708_v2016_n9_p_Donnay
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Black Holes Gauge Symmetry Space-Time Symmetries
spellingShingle	Black Holes Gauge Symmetry Space-Time Symmetries Extended symmetries at the black hole horizon
topic_facet	Black Holes Gauge Symmetry Space-Time Symmetries
description	We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Witt algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature. © 2016, The Author(s).
title	Extended symmetries at the black hole horizon
title_short	Extended symmetries at the black hole horizon
title_full	Extended symmetries at the black hole horizon
title_fullStr	Extended symmetries at the black hole horizon
title_full_unstemmed	Extended symmetries at the black hole horizon
title_sort	extended symmetries at the black hole horizon
publishDate	2016
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11266708_v2016_n9_p_Donnay http://hdl.handle.net/20.500.12110/paper_11266708_v2016_n9_p_Donnay
_version_	1768544696414502912

Extended symmetries at the black hole horizon

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