Thermo Field Dynamics, Boulware and Hartle-Hawking States

Abstract. In this thesis one studied a scalar field over a Schwarzschild background with an integrated interpretation of entanglement, thermo field dynamics formalism and correct ground states, in order to give an explanation of Bekenstein-Hawking entropy and where is located. Using statistical mech...

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Autores:
Muñoz Arboleda, Diego Felipe
Tipo de recurso:
Fecha de publicación:
2017
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/62329
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/62329
http://bdigital.unal.edu.co/61377/
Palabra clave:
51 Matemáticas / Mathematics
52 Astronomía y ciencias afines / Astronomy
53 Física / Physics
Thermo Field Dynamics
Bekenstein-Hawking
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_dc5c0c07365f87504044a79ebd2e3cee
oai_identifier_str oai:repositorio.unal.edu.co:unal/62329
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Thermo Field Dynamics, Boulware and Hartle-Hawking States
title Thermo Field Dynamics, Boulware and Hartle-Hawking States
spellingShingle Thermo Field Dynamics, Boulware and Hartle-Hawking States
51 Matemáticas / Mathematics
52 Astronomía y ciencias afines / Astronomy
53 Física / Physics
Thermo Field Dynamics
Bekenstein-Hawking
title_short Thermo Field Dynamics, Boulware and Hartle-Hawking States
title_full Thermo Field Dynamics, Boulware and Hartle-Hawking States
title_fullStr Thermo Field Dynamics, Boulware and Hartle-Hawking States
title_full_unstemmed Thermo Field Dynamics, Boulware and Hartle-Hawking States
title_sort Thermo Field Dynamics, Boulware and Hartle-Hawking States
dc.creator.fl_str_mv Muñoz Arboleda, Diego Felipe
dc.contributor.author.spa.fl_str_mv Muñoz Arboleda, Diego Felipe
dc.contributor.spa.fl_str_mv Arenas Salazar, Jose Robel
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
52 Astronomía y ciencias afines / Astronomy
53 Física / Physics
topic 51 Matemáticas / Mathematics
52 Astronomía y ciencias afines / Astronomy
53 Física / Physics
Thermo Field Dynamics
Bekenstein-Hawking
dc.subject.proposal.spa.fl_str_mv Thermo Field Dynamics
Bekenstein-Hawking
description Abstract. In this thesis one studied a scalar field over a Schwarzschild background with an integrated interpretation of entanglement, thermo field dynamics formalism and correct ground states, in order to give an explanation of Bekenstein-Hawking entropy and where is located. Using statistical mechanics on a scalar field over a Schwarzschild background one obtain the number of modes of the field and with this, one can find the Helmholtz free energy, which has two terms: one dependent of the volume that is the contribution of the vacuum energy at large distances, and the second one is the contribution of the event horizon to the energy and is proportional to the horizon area. This term diverges when the altitude h tends to zero, ie, very close to the event horizon. This is a reproduction of Gerardus ’tHooft paper [1]. Taking the correct form of h, the total energy U and the entropy S could be obtained. The last one results to be exactly the Bekenstein-Hawking entropy. If one give to a scalar field an operator behavior, and taking into account that above the brick wall there are no horizons, it is possible to see that the correct state of the system in study is the Boulware state. One can conclude that an outside observer can see what it looks like as a black hole but actually does not contain a horizon. Using thermo field dynamic formalism (ThFD) in a quantum scalar field over a eternal Sch- warzschild background one shows that the system meets exactly the characteristics of ThFD, then is a thermal system.
publishDate 2017
dc.date.issued.spa.fl_str_mv 2017-10-24
dc.date.accessioned.spa.fl_str_mv 2019-07-02T20:57:18Z
dc.date.available.spa.fl_str_mv 2019-07-02T20:57:18Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/62329
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/61377/
url https://repositorio.unal.edu.co/handle/unal/62329
http://bdigital.unal.edu.co/61377/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Física
Departamento de Física
dc.relation.references.spa.fl_str_mv Muñoz Arboleda, Diego Felipe (2017) Thermo Field Dynamics, Boulware and Hartle-Hawking States. Maestría thesis, Universidad Nacional de Colombia-Sede Bogotá.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
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institution Universidad Nacional de Colombia
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Arenas Salazar, Jose RobelMuñoz Arboleda, Diego Felipe56b52b84-6ce4-49e7-a8f1-4579aa0976c13002019-07-02T20:57:18Z2019-07-02T20:57:18Z2017-10-24https://repositorio.unal.edu.co/handle/unal/62329http://bdigital.unal.edu.co/61377/Abstract. In this thesis one studied a scalar field over a Schwarzschild background with an integrated interpretation of entanglement, thermo field dynamics formalism and correct ground states, in order to give an explanation of Bekenstein-Hawking entropy and where is located. Using statistical mechanics on a scalar field over a Schwarzschild background one obtain the number of modes of the field and with this, one can find the Helmholtz free energy, which has two terms: one dependent of the volume that is the contribution of the vacuum energy at large distances, and the second one is the contribution of the event horizon to the energy and is proportional to the horizon area. This term diverges when the altitude h tends to zero, ie, very close to the event horizon. This is a reproduction of Gerardus ’tHooft paper [1]. Taking the correct form of h, the total energy U and the entropy S could be obtained. The last one results to be exactly the Bekenstein-Hawking entropy. If one give to a scalar field an operator behavior, and taking into account that above the brick wall there are no horizons, it is possible to see that the correct state of the system in study is the Boulware state. One can conclude that an outside observer can see what it looks like as a black hole but actually does not contain a horizon. Using thermo field dynamic formalism (ThFD) in a quantum scalar field over a eternal Sch- warzschild background one shows that the system meets exactly the characteristics of ThFD, then is a thermal system.En esta tesis se estudió un campo escalar sobre un fondo tipo Schwarzschild con una inter- pretación integrada de entanglamiento, formalismo de dinámica de campos térmicos y una correcta escogencia de los estados de vacı́o, con el fin de dar una explicación a la entropı́a de Bekenstein-Hawking y en donde se puede localizar. Utilizando mecánica estadı́stica en un campo escalar sobre el fondo de Scwrzschild uno ob- tiene el número de modos de campo y con esto, es posible encontrar a energı́a libre de Helm- holtz, la cual tiene dos términos: Uno dependiente del volumen, el cual es la contribución a la energı́a de vacı́o a grandes distancias, el segundo término corresponde a la contribución de la energı́a al horizonte de eventos y es proporcional al área del horizonte. Esta es una reproducción del artı́culo de Gerardus ’tHooft [1]. Tomando la forma correcta de h, se ob- x tienen la energı́a total U y la entropı́a S. La última resulta ser exáctamente la entropı́a de Bekenstein-Hawking. Si uno le da un comportamiento tipo operador al campo escalar y se tiene en cuenta que encima del Brick Wall no hay horizontes, es posible ver que el estado correcto del sistema en estudio es el estado de Boulware. Se puede concluir que un observador externo puede ver lo que parece ser un agujero negro pero en realidad no contiene un horizonte. Usando dinámica de campos térmicos (ThFD) para un campo escalar cuántico sobre un agujero negro de Schwarzschild eterno uno muestra que el sistema tiene las mismas caracterı́sticas de ThFD, por lo tanto el sistema es térmico.Maestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de FísicaDepartamento de FísicaMuñoz Arboleda, Diego Felipe (2017) Thermo Field Dynamics, Boulware and Hartle-Hawking States. Maestría thesis, Universidad Nacional de Colombia-Sede Bogotá.51 Matemáticas / Mathematics52 Astronomía y ciencias afines / Astronomy53 Física / PhysicsThermo Field DynamicsBekenstein-HawkingThermo Field Dynamics, Boulware and Hartle-Hawking StatesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINALDiegoF.MunozArboleda.2017.pdfapplication/pdf683407https://repositorio.unal.edu.co/bitstream/unal/62329/1/DiegoF.MunozArboleda.2017.pdf3984ff9a40c417fd89eda5ae4a81d859MD51THUMBNAILDiegoF.MunozArboleda.2017.pdf.jpgDiegoF.MunozArboleda.2017.pdf.jpgGenerated Thumbnailimage/jpeg4046https://repositorio.unal.edu.co/bitstream/unal/62329/2/DiegoF.MunozArboleda.2017.pdf.jpg81ab70d173d6811b03ddd0dda17b50b8MD52unal/62329oai:repositorio.unal.edu.co:unal/623292023-04-16 23:05:35.237Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co

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