The area-angular momentum inequality for black holes in cosmological spacetimes

Autores
Gabach Clement, Maria Eugenia; Reiris, Martín; Simon, Walter
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
For a stable, marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant λ > 0 and with matter satisfying the dominant energy condition, we prove that the area A and the angular momentum J satisfy the inequality 8π|J| ≤ A√(1 - λA/4π)(1 - λA/12π), which is saturated precisely for the extreme Kerr-de Sitter family of metrics. This result entails a universal upper bound |J| ≤ Jmax ≈ 0.17/λ for such MOTS, which is saturated for one particular extreme configuration. Our result sharpens the inequality 8π |J| ≤ A (Dain and Reiris 2011 Phys. Rev. Lett. 107 051101, Jaramillo, Reiris and Dain 2011 Phys. Rev. Lett. D 84 121503), and we follow the overall strategy of its proof in the sense that we first estimate the area from below in terms of the energy corresponding to a 'mass functional', which is basically a suitably regularized harmonic map S2 → H2. However, in the cosmological case this mass functional acquires an additional potential term which itself depends on the area. To estimate the corresponding energy in terms of the angular momentum and the cosmological constant we use a subtle scaling argument, a generalized 'Carter-identity', and various techniques from variational calculus, including the mountain pass theorem.
Fil: Gabach Clement, Maria Eugenia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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
Fil: Reiris, Martín. Max Planck Fuer Gravitationsphysik (aei); Alemania
Fil: Simon, Walter. Universidad de Viena; Austria
Materia
Apparent Horizon
Area Inequality
Cosmological Constant
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:11336/51216
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The area-angular momentum inequality for black holes in cosmological spacetimesGabach Clement, Maria EugeniaReiris, MartínSimon, WalterApparent HorizonArea InequalityCosmological Constanthttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1For a stable, marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant λ > 0 and with matter satisfying the dominant energy condition, we prove that the area A and the angular momentum J satisfy the inequality 8π|J| ≤ A√(1 - λA/4π)(1 - λA/12π), which is saturated precisely for the extreme Kerr-de Sitter family of metrics. This result entails a universal upper bound |J| ≤ Jmax ≈ 0.17/λ for such MOTS, which is saturated for one particular extreme configuration. Our result sharpens the inequality 8π |J| ≤ A (Dain and Reiris 2011 Phys. Rev. Lett. 107 051101, Jaramillo, Reiris and Dain 2011 Phys. Rev. Lett. D 84 121503), and we follow the overall strategy of its proof in the sense that we first estimate the area from below in terms of the energy corresponding to a 'mass functional', which is basically a suitably regularized harmonic map S2 → H2. However, in the cosmological case this mass functional acquires an additional potential term which itself depends on the area. To estimate the corresponding energy in terms of the angular momentum and the cosmological constant we use a subtle scaling argument, a generalized 'Carter-identity', and various techniques from variational calculus, including the mountain pass theorem.Fil: Gabach Clement, Maria Eugenia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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; ArgentinaFil: Reiris, Martín. Max Planck Fuer Gravitationsphysik (aei); AlemaniaFil: Simon, Walter. Universidad de Viena; AustriaIOP Publishing2015-07info: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/11336/51216Gabach Clement, Maria Eugenia; Reiris, Martín; Simon, Walter; The area-angular momentum inequality for black holes in cosmological spacetimes; IOP Publishing; Classical and Quantum Gravity; 32; 14; 7-20150264-93811361-6382CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0264-9381/32/14/145006info:eu-repo/semantics/altIdentifier/doi/10.1088/0264-9381/32/14/145006info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:59:42Zoai:ri.conicet.gov.ar:11336/51216instacron: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 11:59:42.297CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The area-angular momentum inequality for black holes in cosmological spacetimes
title The area-angular momentum inequality for black holes in cosmological spacetimes
spellingShingle The area-angular momentum inequality for black holes in cosmological spacetimes
Gabach Clement, Maria Eugenia
Apparent Horizon
Area Inequality
Cosmological Constant
title_short The area-angular momentum inequality for black holes in cosmological spacetimes
title_full The area-angular momentum inequality for black holes in cosmological spacetimes
title_fullStr The area-angular momentum inequality for black holes in cosmological spacetimes
title_full_unstemmed The area-angular momentum inequality for black holes in cosmological spacetimes
title_sort The area-angular momentum inequality for black holes in cosmological spacetimes
dc.creator.none.fl_str_mv Gabach Clement, Maria Eugenia
Reiris, Martín
Simon, Walter
author Gabach Clement, Maria Eugenia
author_facet Gabach Clement, Maria Eugenia
Reiris, Martín
Simon, Walter
author_role author
author2 Reiris, Martín
Simon, Walter
author2_role author
author
dc.subject.none.fl_str_mv Apparent Horizon
Area Inequality
Cosmological Constant
topic Apparent Horizon
Area Inequality
Cosmological Constant
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv For a stable, marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant λ > 0 and with matter satisfying the dominant energy condition, we prove that the area A and the angular momentum J satisfy the inequality 8π|J| ≤ A√(1 - λA/4π)(1 - λA/12π), which is saturated precisely for the extreme Kerr-de Sitter family of metrics. This result entails a universal upper bound |J| ≤ Jmax ≈ 0.17/λ for such MOTS, which is saturated for one particular extreme configuration. Our result sharpens the inequality 8π |J| ≤ A (Dain and Reiris 2011 Phys. Rev. Lett. 107 051101, Jaramillo, Reiris and Dain 2011 Phys. Rev. Lett. D 84 121503), and we follow the overall strategy of its proof in the sense that we first estimate the area from below in terms of the energy corresponding to a 'mass functional', which is basically a suitably regularized harmonic map S2 → H2. However, in the cosmological case this mass functional acquires an additional potential term which itself depends on the area. To estimate the corresponding energy in terms of the angular momentum and the cosmological constant we use a subtle scaling argument, a generalized 'Carter-identity', and various techniques from variational calculus, including the mountain pass theorem.
Fil: Gabach Clement, Maria Eugenia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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
Fil: Reiris, Martín. Max Planck Fuer Gravitationsphysik (aei); Alemania
Fil: Simon, Walter. Universidad de Viena; Austria
description For a stable, marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant λ > 0 and with matter satisfying the dominant energy condition, we prove that the area A and the angular momentum J satisfy the inequality 8π|J| ≤ A√(1 - λA/4π)(1 - λA/12π), which is saturated precisely for the extreme Kerr-de Sitter family of metrics. This result entails a universal upper bound |J| ≤ Jmax ≈ 0.17/λ for such MOTS, which is saturated for one particular extreme configuration. Our result sharpens the inequality 8π |J| ≤ A (Dain and Reiris 2011 Phys. Rev. Lett. 107 051101, Jaramillo, Reiris and Dain 2011 Phys. Rev. Lett. D 84 121503), and we follow the overall strategy of its proof in the sense that we first estimate the area from below in terms of the energy corresponding to a 'mass functional', which is basically a suitably regularized harmonic map S2 → H2. However, in the cosmological case this mass functional acquires an additional potential term which itself depends on the area. To estimate the corresponding energy in terms of the angular momentum and the cosmological constant we use a subtle scaling argument, a generalized 'Carter-identity', and various techniques from variational calculus, including the mountain pass theorem.
publishDate 2015
dc.date.none.fl_str_mv 2015-07
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/11336/51216
Gabach Clement, Maria Eugenia; Reiris, Martín; Simon, Walter; The area-angular momentum inequality for black holes in cosmological spacetimes; IOP Publishing; Classical and Quantum Gravity; 32; 14; 7-2015
0264-9381
1361-6382
CONICET Digital
CONICET
url http://hdl.handle.net/11336/51216
identifier_str_mv Gabach Clement, Maria Eugenia; Reiris, Martín; Simon, Walter; The area-angular momentum inequality for black holes in cosmological spacetimes; IOP Publishing; Classical and Quantum Gravity; 32; 14; 7-2015
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/url/http://iopscience.iop.org/article/10.1088/0264-9381/32/14/145006
info:eu-repo/semantics/altIdentifier/doi/10.1088/0264-9381/32/14/145006
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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