Black hole non-modal linear stability: The Schwarzschild (A)dS cases

Autores
Dotti, Gustavo Daniel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The non-modal linear stability of the Schwarzschild black hole established in Dotti (2014 Phys. Rev. Lett. 112 191101) is generalized to the case of a non-negative cosmological constant Λ. Two gauge invariant combinations G± of perturbed scalars made out of the Weyl tensor and its first covariant derivative are found such that the map with domain the set of equivalent classes under gauge transformations of solutions of the linearized Einstein's equation, is invertible. The way to reconstruct a representative of in terms of is given. It is proved that, for an arbitrary perturbation consistent with the background asymptote, and are bounded in the the outer static region. At large times, the perturbation decays leaving a linearized Kerr black hole around the Schwarzschild or Schwarschild de Sitter background solution. For negative cosmological constant it is shown that there are choices of boundary conditions at the time-like boundary under which the Schwarzschild anti de Sitter black hole is unstable. The root of Chandrasekhar's duality relating odd and even modes is exhibited, and some technicalities related to this duality and omitted in the original proof of the case are explained in detail.
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
BLACK HOLES
LINEAR STABILITY
MEASURABLE EFFECTS OF PERTURBATIONS
NON-MODAL APPROACH
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:11336/73291
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/73291
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Black hole non-modal linear stability: The Schwarzschild (A)dS casesDotti, Gustavo DanielBLACK HOLESLINEAR STABILITYMEASURABLE EFFECTS OF PERTURBATIONSNON-MODAL APPROACHhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The non-modal linear stability of the Schwarzschild black hole established in Dotti (2014 Phys. Rev. Lett. 112 191101) is generalized to the case of a non-negative cosmological constant Λ. Two gauge invariant combinations G± of perturbed scalars made out of the Weyl tensor and its first covariant derivative are found such that the map with domain the set of equivalent classes under gauge transformations of solutions of the linearized Einstein's equation, is invertible. The way to reconstruct a representative of in terms of is given. It is proved that, for an arbitrary perturbation consistent with the background asymptote, and are bounded in the the outer static region. At large times, the perturbation decays leaving a linearized Kerr black hole around the Schwarzschild or Schwarschild de Sitter background solution. For negative cosmological constant it is shown that there are choices of boundary conditions at the time-like boundary under which the Schwarzschild anti de Sitter black hole is unstable. The root of Chandrasekhar's duality relating odd and even modes is exhibited, and some technicalities related to this duality and omitted in the original proof of the case are explained in detail.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; ArgentinaIOP Publishing2016-09-21info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/73291Dotti, Gustavo Daniel; Black hole non-modal linear stability: The Schwarzschild (A)dS cases; IOP Publishing; Classical and Quantum Gravity; 33; 20; 21-9-2016; 1-430264-93811361-6382CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/0264-9381/33/20/205005info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1603.03749info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/0264-9381/33/20/205005/metainfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:54:46Zoai:ri.conicet.gov.ar:11336/73291instacron: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:34982025-10-22 11:54:46.91CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Black hole non-modal linear stability: The Schwarzschild (A)dS cases
title Black hole non-modal linear stability: The Schwarzschild (A)dS cases
spellingShingle Black hole non-modal linear stability: The Schwarzschild (A)dS cases
Dotti, Gustavo Daniel
BLACK HOLES
LINEAR STABILITY
MEASURABLE EFFECTS OF PERTURBATIONS
NON-MODAL APPROACH
title_short Black hole non-modal linear stability: The Schwarzschild (A)dS cases
title_full Black hole non-modal linear stability: The Schwarzschild (A)dS cases
title_fullStr Black hole non-modal linear stability: The Schwarzschild (A)dS cases
title_full_unstemmed Black hole non-modal linear stability: The Schwarzschild (A)dS cases
title_sort Black hole non-modal linear stability: The Schwarzschild (A)dS cases
dc.creator.none.fl_str_mv Dotti, Gustavo Daniel
author Dotti, Gustavo Daniel
author_facet Dotti, Gustavo Daniel
author_role author
dc.subject.none.fl_str_mv BLACK HOLES
LINEAR STABILITY
MEASURABLE EFFECTS OF PERTURBATIONS
NON-MODAL APPROACH
topic BLACK HOLES
LINEAR STABILITY
MEASURABLE EFFECTS OF PERTURBATIONS
NON-MODAL APPROACH
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 non-modal linear stability of the Schwarzschild black hole established in Dotti (2014 Phys. Rev. Lett. 112 191101) is generalized to the case of a non-negative cosmological constant Λ. Two gauge invariant combinations G± of perturbed scalars made out of the Weyl tensor and its first covariant derivative are found such that the map with domain the set of equivalent classes under gauge transformations of solutions of the linearized Einstein's equation, is invertible. The way to reconstruct a representative of in terms of is given. It is proved that, for an arbitrary perturbation consistent with the background asymptote, and are bounded in the the outer static region. At large times, the perturbation decays leaving a linearized Kerr black hole around the Schwarzschild or Schwarschild de Sitter background solution. For negative cosmological constant it is shown that there are choices of boundary conditions at the time-like boundary under which the Schwarzschild anti de Sitter black hole is unstable. The root of Chandrasekhar's duality relating odd and even modes is exhibited, and some technicalities related to this duality and omitted in the original proof of the case are explained in detail.
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 non-modal linear stability of the Schwarzschild black hole established in Dotti (2014 Phys. Rev. Lett. 112 191101) is generalized to the case of a non-negative cosmological constant Λ. Two gauge invariant combinations G± of perturbed scalars made out of the Weyl tensor and its first covariant derivative are found such that the map with domain the set of equivalent classes under gauge transformations of solutions of the linearized Einstein's equation, is invertible. The way to reconstruct a representative of in terms of is given. It is proved that, for an arbitrary perturbation consistent with the background asymptote, and are bounded in the the outer static region. At large times, the perturbation decays leaving a linearized Kerr black hole around the Schwarzschild or Schwarschild de Sitter background solution. For negative cosmological constant it is shown that there are choices of boundary conditions at the time-like boundary under which the Schwarzschild anti de Sitter black hole is unstable. The root of Chandrasekhar's duality relating odd and even modes is exhibited, and some technicalities related to this duality and omitted in the original proof of the case are explained in detail.
publishDate 2016
dc.date.none.fl_str_mv 2016-09-21
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/11336/73291
Dotti, Gustavo Daniel; Black hole non-modal linear stability: The Schwarzschild (A)dS cases; IOP Publishing; Classical and Quantum Gravity; 33; 20; 21-9-2016; 1-43
0264-9381
1361-6382
CONICET Digital
CONICET
url http://hdl.handle.net/11336/73291
identifier_str_mv Dotti, Gustavo Daniel; Black hole non-modal linear stability: The Schwarzschild (A)dS cases; IOP Publishing; Classical and Quantum Gravity; 33; 20; 21-9-2016; 1-43
0264-9381
1361-6382
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/0264-9381/33/20/205005
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1603.03749
info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/0264-9381/33/20/205005/meta
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
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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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score 12.982451

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