Bose-Einstein graviton condensate in a Schwarzschild black hole

We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose-Einstein condensate of gravitons. In order to do so we extend the Einstein-Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. T...

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Detalles Bibliográficos
Autores: Alfaro, Jorge, Espriu, D. (Domènec), Gabbanelli, Luciano
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/142927
Acceso en línea:https://hdl.handle.net/2445/142927
Access Level:acceso abierto
Palabra clave:Condensació de Bose-Einstein
Forats negres (Astronomia)
Bose-Einstein condensation
Black holes (Astronomy)
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spelling Bose-Einstein graviton condensate in a Schwarzschild black holeAlfaro, JorgeEspriu, D. (Domènec)Gabbanelli, LucianoCondensació de Bose-EinsteinForats negres (Astronomia)Bose-Einstein condensationBlack holes (Astronomy)We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose-Einstein condensate of gravitons. In order to do so we extend the Einstein-Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross-Pitaevskii equation describing a graviton Bose-Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose-Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons N and the black hole characteristics along the lines suggested by Dvali and Gómez.Institute of Physics (IOP)2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/142927Articles publicats en revistes (Física Quàntica i Astrofísica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1088/1361-6382/aa9771Classical and Quantum Gravity, 2018, vol. 35, num. 1https://doi.org/10.1088/1361-6382/aa9771info:eu-repo/grantAgreement/EC/FP7/246806cc-by-nc-nd (c) Institute of Physics (IOP), 2018http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1429272026-05-27T06:46:51Z
dc.title.none.fl_str_mv Bose-Einstein graviton condensate in a Schwarzschild black hole
title Bose-Einstein graviton condensate in a Schwarzschild black hole
spellingShingle Bose-Einstein graviton condensate in a Schwarzschild black hole
Alfaro, Jorge
Condensació de Bose-Einstein
Forats negres (Astronomia)
Bose-Einstein condensation
Black holes (Astronomy)
title_short Bose-Einstein graviton condensate in a Schwarzschild black hole
title_full Bose-Einstein graviton condensate in a Schwarzschild black hole
title_fullStr Bose-Einstein graviton condensate in a Schwarzschild black hole
title_full_unstemmed Bose-Einstein graviton condensate in a Schwarzschild black hole
title_sort Bose-Einstein graviton condensate in a Schwarzschild black hole
dc.creator.none.fl_str_mv Alfaro, Jorge
Espriu, D. (Domènec)
Gabbanelli, Luciano
author Alfaro, Jorge
author_facet Alfaro, Jorge
Espriu, D. (Domènec)
Gabbanelli, Luciano
author_role author
author2 Espriu, D. (Domènec)
Gabbanelli, Luciano
author2_role author
author
dc.subject.none.fl_str_mv Condensació de Bose-Einstein
Forats negres (Astronomia)
Bose-Einstein condensation
Black holes (Astronomy)
topic Condensació de Bose-Einstein
Forats negres (Astronomia)
Bose-Einstein condensation
Black holes (Astronomy)
description We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose-Einstein condensate of gravitons. In order to do so we extend the Einstein-Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross-Pitaevskii equation describing a graviton Bose-Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose-Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons N and the black hole characteristics along the lines suggested by Dvali and Gómez.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/142927
url https://hdl.handle.net/2445/142927
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1088/1361-6382/aa9771
Classical and Quantum Gravity, 2018, vol. 35, num. 1
https://doi.org/10.1088/1361-6382/aa9771
info:eu-repo/grantAgreement/EC/FP7/246806
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Institute of Physics (IOP), 2018
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Institute of Physics (IOP), 2018
http://creativecommons.org/licenses/by-nc-nd/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Institute of Physics (IOP)
publisher.none.fl_str_mv Institute of Physics (IOP)
dc.source.none.fl_str_mv Articles publicats en revistes (Física Quàntica i Astrofísica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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