Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary

Autores
Araneda, Bernardo Gabriel; Dotti, Gustavo Daniel
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The static region outside the event horizon of an asymptotically anti-de Sitter black hole has a conformal timelike boundary I on which boundary conditions have to be imposed for the evolution of linear fields from initial data to be a well-posed problem. Only homogeneous Dirichlet, Neumann or Robin conditions preserve the action of the background isometry group on the solution space. We study the case in which the modal decomposition of the linear field leads to potentials not diverging at the conformal timelike boundary. We prove that there is always an instability if Robin boundary conditions with large enough γ (the quotient between the values of the derivative of the field and the field at the boundary) are allowed. We explain the origin of this instability, show that for modes with non-negative potentials there is a single unstable state and prove a number of properties of this state. Although our results apply, in general, to 1+1 wave equations on a half-infinite domain with a potential that is not singular at the boundary, our motivation is to analyze the gravitational stability of the four-dimensional Schwarzschild anti-de Sitter black holes in the context of the black hole nonmodal linear stability program initiated in Phys. Rev. Lett. 112, 191101 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.191101, and the related supersymmetric type of duality exchanging odd and even modes. We prove that this symmetry is broken except when a combination of Dirichlet conditions in the even sector and a particular Robin condition in the odd sector is enforced, or vice versa, and that only the first of these two choices leads to stable dynamics.
Fil: Araneda, Bernardo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Dotti, Gustavo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
Anti de sitter black holes
Perturbations
Boundary Conditions
Instabilities
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/64728

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network_name_str CONICET Digital (CONICET)
spelling Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundaryAraneda, Bernardo GabrielDotti, Gustavo DanielAnti de sitter black holesPerturbationsBoundary ConditionsInstabilitieshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The static region outside the event horizon of an asymptotically anti-de Sitter black hole has a conformal timelike boundary I on which boundary conditions have to be imposed for the evolution of linear fields from initial data to be a well-posed problem. Only homogeneous Dirichlet, Neumann or Robin conditions preserve the action of the background isometry group on the solution space. We study the case in which the modal decomposition of the linear field leads to potentials not diverging at the conformal timelike boundary. We prove that there is always an instability if Robin boundary conditions with large enough γ (the quotient between the values of the derivative of the field and the field at the boundary) are allowed. We explain the origin of this instability, show that for modes with non-negative potentials there is a single unstable state and prove a number of properties of this state. Although our results apply, in general, to 1+1 wave equations on a half-infinite domain with a potential that is not singular at the boundary, our motivation is to analyze the gravitational stability of the four-dimensional Schwarzschild anti-de Sitter black holes in the context of the black hole nonmodal linear stability program initiated in Phys. Rev. Lett. 112, 191101 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.191101, and the related supersymmetric type of duality exchanging odd and even modes. We prove that this symmetry is broken except when a combination of Dirichlet conditions in the even sector and a particular Robin condition in the odd sector is enforced, or vice versa, and that only the first of these two choices leads to stable dynamics.Fil: Araneda, Bernardo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Dotti, Gustavo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaAmerican Physical Society2017-11-15info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/64728Araneda, Bernardo Gabriel; Dotti, Gustavo Daniel; Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary; American Physical Society; Physical Review D; 96; 10; 15-11-2017; 1-222470-00292470-0010CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevD.96.104020info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.96.104020info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1611.03534info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:58:39Zoai:ri.conicet.gov.ar:11336/64728instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:58:39.511CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary
title Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary
spellingShingle Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary
Araneda, Bernardo Gabriel
Anti de sitter black holes
Perturbations
Boundary Conditions
Instabilities
title_short Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary
title_full Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary
title_fullStr Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary
title_full_unstemmed Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary
title_sort Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary
dc.creator.none.fl_str_mv Araneda, Bernardo Gabriel
Dotti, Gustavo Daniel
author Araneda, Bernardo Gabriel
author_facet Araneda, Bernardo Gabriel
Dotti, Gustavo Daniel
author_role author
author2 Dotti, Gustavo Daniel
author2_role author
dc.subject.none.fl_str_mv Anti de sitter black holes
Perturbations
Boundary Conditions
Instabilities
topic Anti de sitter black holes
Perturbations
Boundary Conditions
Instabilities
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The static region outside the event horizon of an asymptotically anti-de Sitter black hole has a conformal timelike boundary I on which boundary conditions have to be imposed for the evolution of linear fields from initial data to be a well-posed problem. Only homogeneous Dirichlet, Neumann or Robin conditions preserve the action of the background isometry group on the solution space. We study the case in which the modal decomposition of the linear field leads to potentials not diverging at the conformal timelike boundary. We prove that there is always an instability if Robin boundary conditions with large enough γ (the quotient between the values of the derivative of the field and the field at the boundary) are allowed. We explain the origin of this instability, show that for modes with non-negative potentials there is a single unstable state and prove a number of properties of this state. Although our results apply, in general, to 1+1 wave equations on a half-infinite domain with a potential that is not singular at the boundary, our motivation is to analyze the gravitational stability of the four-dimensional Schwarzschild anti-de Sitter black holes in the context of the black hole nonmodal linear stability program initiated in Phys. Rev. Lett. 112, 191101 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.191101, and the related supersymmetric type of duality exchanging odd and even modes. We prove that this symmetry is broken except when a combination of Dirichlet conditions in the even sector and a particular Robin condition in the odd sector is enforced, or vice versa, and that only the first of these two choices leads to stable dynamics.
Fil: Araneda, Bernardo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Dotti, Gustavo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description The static region outside the event horizon of an asymptotically anti-de Sitter black hole has a conformal timelike boundary I on which boundary conditions have to be imposed for the evolution of linear fields from initial data to be a well-posed problem. Only homogeneous Dirichlet, Neumann or Robin conditions preserve the action of the background isometry group on the solution space. We study the case in which the modal decomposition of the linear field leads to potentials not diverging at the conformal timelike boundary. We prove that there is always an instability if Robin boundary conditions with large enough γ (the quotient between the values of the derivative of the field and the field at the boundary) are allowed. We explain the origin of this instability, show that for modes with non-negative potentials there is a single unstable state and prove a number of properties of this state. Although our results apply, in general, to 1+1 wave equations on a half-infinite domain with a potential that is not singular at the boundary, our motivation is to analyze the gravitational stability of the four-dimensional Schwarzschild anti-de Sitter black holes in the context of the black hole nonmodal linear stability program initiated in Phys. Rev. Lett. 112, 191101 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.191101, and the related supersymmetric type of duality exchanging odd and even modes. We prove that this symmetry is broken except when a combination of Dirichlet conditions in the even sector and a particular Robin condition in the odd sector is enforced, or vice versa, and that only the first of these two choices leads to stable dynamics.
publishDate 2017
dc.date.none.fl_str_mv 2017-11-15
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/64728
Araneda, Bernardo Gabriel; Dotti, Gustavo Daniel; Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary; American Physical Society; Physical Review D; 96; 10; 15-11-2017; 1-22
2470-0029
2470-0010
CONICET Digital
CONICET
url http://hdl.handle.net/11336/64728
identifier_str_mv Araneda, Bernardo Gabriel; Dotti, Gustavo Daniel; Instability of asymptotically anti-de Sitter black holes under Robin conditions at the timelike boundary; American Physical Society; Physical Review D; 96; 10; 15-11-2017; 1-22
2470-0029
2470-0010
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevD.96.104020
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.96.104020
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1611.03534
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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