Thermodynamic properties of causal horizons
Autor(a) principal: | |
---|---|
Data de Publicação: | 2020 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://www.teses.usp.br/teses/disponiveis/76/76134/tde-27052020-191622/ |
Resumo: | Black hole thermodynamics emerged as a surprising connection between thermodynamics and general relativity, showing that one may attribute properties like entropy and temperature to a black hole´s event horizon. Inspired by it, studies from the last decades indicate that this analogy extends itself to many models and systems in which one considers the existence of causal horizons. Given certain assumptions, it is even possible to derive Einstein´s field equations from the laws of thermodynamics. Nevertheless, this result was not constructed on foundations so solid as those of black hole thermodynamics, leaving room for a formalization of these ideas. Therefore, in order to advance in the generalization of the relation between thermodynamics and gravitation, one may focus on the study of the geometry of causal horizons, which correspond to lightlike hypersurfaces of a spacetime. In this work, we review the laws of black hole thermodynamics, giving special attention to the generalized second law, and show how the mentioned analogy is formulated for general causal horizons. Then, we present the induced geometric objects on lightlike hypersurfaces, providing the basic mathematical tools to analyze the geometry of causal horizons. |
id |
USP_e7f4002b12f9aa02c95a85a3345b8bef |
---|---|
oai_identifier_str |
oai:teses.usp.br:tde-27052020-191622 |
network_acronym_str |
USP |
network_name_str |
Biblioteca Digital de Teses e Dissertações da USP |
repository_id_str |
2721 |
spelling |
Thermodynamic properties of causal horizonsPropriedades termodinâmicas de horizontes causaisBlack hole thermodynamicsCausal horizonsHipersuperfícies tipo-luzHorizontes causaisLightlike hypersurfacesTermodinâmica de buracos negrosBlack hole thermodynamics emerged as a surprising connection between thermodynamics and general relativity, showing that one may attribute properties like entropy and temperature to a black hole´s event horizon. Inspired by it, studies from the last decades indicate that this analogy extends itself to many models and systems in which one considers the existence of causal horizons. Given certain assumptions, it is even possible to derive Einstein´s field equations from the laws of thermodynamics. Nevertheless, this result was not constructed on foundations so solid as those of black hole thermodynamics, leaving room for a formalization of these ideas. Therefore, in order to advance in the generalization of the relation between thermodynamics and gravitation, one may focus on the study of the geometry of causal horizons, which correspond to lightlike hypersurfaces of a spacetime. In this work, we review the laws of black hole thermodynamics, giving special attention to the generalized second law, and show how the mentioned analogy is formulated for general causal horizons. Then, we present the induced geometric objects on lightlike hypersurfaces, providing the basic mathematical tools to analyze the geometry of causal horizons.A termodinâmica de buracos negros surgiu como uma surpreendente conexão entre termodinâmica e relatividade geral, mostrando que é possível atribuir propriedades como entropia e temperatura ao horizonte de eventos de um buraco negro. Inspirados por ela, estudos feitos nas últimas décadas indicam que esta analogia se estende para muitos modelos e sistemas nos quais é considerada a existência de horizontes causais. Dadas certas suposições, é possível inclusive derivar as equações de campo de Einstein a partir das leis da termodinâmica. Contudo, tal resultado não foi construído sobre bases tão sólidas quanto aquelas da termodinâmica de buracos negros, abrindo espaço para uma formalização destas ideias. Desta forma, a fim de avançar na generalização da relação entre termodinâmica e gravitação, é possível focar no estudo da geometria de horizontes causais, os quais correspondem a hipersuperfícies tipo-luz de um espaço-tempo. Neste trabalho, serão revisadas as leis da termodinâmica de buracos negros, dando atenção especial para a segunda lei generalizada, e será mostrado como a analogia mencionada é formulada para horizontes causais genéricos. Em seguida, serão apresentados os objetos geométricos induzidos em hipersuperfícies tipo-luz, fornecendo as ferramentas matemáticas básicas para analisar a geometria de horizontes causais.Biblioteca Digitais de Teses e Dissertações da USPVanzela, Daniel Augusto TurollaBarbosa, Matheus Goulart2020-02-20info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttps://www.teses.usp.br/teses/disponiveis/76/76134/tde-27052020-191622/reponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USPLiberar o conteúdo para acesso público.info:eu-repo/semantics/openAccesseng2024-08-23T14:49:02Zoai:teses.usp.br:tde-27052020-191622Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212024-08-23T14:49:02Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.none.fl_str_mv |
Thermodynamic properties of causal horizons Propriedades termodinâmicas de horizontes causais |
title |
Thermodynamic properties of causal horizons |
spellingShingle |
Thermodynamic properties of causal horizons Barbosa, Matheus Goulart Black hole thermodynamics Causal horizons Hipersuperfícies tipo-luz Horizontes causais Lightlike hypersurfaces Termodinâmica de buracos negros |
title_short |
Thermodynamic properties of causal horizons |
title_full |
Thermodynamic properties of causal horizons |
title_fullStr |
Thermodynamic properties of causal horizons |
title_full_unstemmed |
Thermodynamic properties of causal horizons |
title_sort |
Thermodynamic properties of causal horizons |
author |
Barbosa, Matheus Goulart |
author_facet |
Barbosa, Matheus Goulart |
author_role |
author |
dc.contributor.none.fl_str_mv |
Vanzela, Daniel Augusto Turolla |
dc.contributor.author.fl_str_mv |
Barbosa, Matheus Goulart |
dc.subject.por.fl_str_mv |
Black hole thermodynamics Causal horizons Hipersuperfícies tipo-luz Horizontes causais Lightlike hypersurfaces Termodinâmica de buracos negros |
topic |
Black hole thermodynamics Causal horizons Hipersuperfícies tipo-luz Horizontes causais Lightlike hypersurfaces Termodinâmica de buracos negros |
description |
Black hole thermodynamics emerged as a surprising connection between thermodynamics and general relativity, showing that one may attribute properties like entropy and temperature to a black hole´s event horizon. Inspired by it, studies from the last decades indicate that this analogy extends itself to many models and systems in which one considers the existence of causal horizons. Given certain assumptions, it is even possible to derive Einstein´s field equations from the laws of thermodynamics. Nevertheless, this result was not constructed on foundations so solid as those of black hole thermodynamics, leaving room for a formalization of these ideas. Therefore, in order to advance in the generalization of the relation between thermodynamics and gravitation, one may focus on the study of the geometry of causal horizons, which correspond to lightlike hypersurfaces of a spacetime. In this work, we review the laws of black hole thermodynamics, giving special attention to the generalized second law, and show how the mentioned analogy is formulated for general causal horizons. Then, we present the induced geometric objects on lightlike hypersurfaces, providing the basic mathematical tools to analyze the geometry of causal horizons. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-02-20 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://www.teses.usp.br/teses/disponiveis/76/76134/tde-27052020-191622/ |
url |
https://www.teses.usp.br/teses/disponiveis/76/76134/tde-27052020-191622/ |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
|
dc.rights.driver.fl_str_mv |
Liberar o conteúdo para acesso público. info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Liberar o conteúdo para acesso público. |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.coverage.none.fl_str_mv |
|
dc.publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
_version_ |
1809091123494256640 |