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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/64728
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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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1844613746540937216 |
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13.070432 |