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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/51216
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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 Técnicas2025-09-29T10:27:08Zoai: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:34982025-09-29 10:27:08.507CONICET 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/ |
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dc.publisher.none.fl_str_mv |
IOP Publishing |
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IOP Publishing |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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