On symmetries of exact solutions of Einstein field equations

Detalhes bibliográficos
Autor(a) principal: ALMEIDA, Gabriel Luz
Data de Publicação: 2019
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional da UFPE
dARK ID: ark:/64986/0013000014t71
Texto Completo: https://repositorio.ufpe.br/handle/123456789/34291
Resumo: SILVA FILHO, Carlos Alberto Batista da, também é conhecido em citações bibliográficas por: BATISTA, Carlos
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spelling ALMEIDA, Gabriel Luzhttp://lattes.cnpq.br/4974855586479672http://lattes.cnpq.br/0760705959572749SILVA FILHO, Carlos Alberto Batista da2019-10-08T17:06:27Z2019-10-08T17:06:27Z2019-06-27https://repositorio.ufpe.br/handle/123456789/34291ark:/64986/0013000014t71SILVA FILHO, Carlos Alberto Batista da, também é conhecido em citações bibliográficas por: BATISTA, CarlosIn this dissertation, symmetries are studied in the context of general relativity. Initially, we address the problem of separability of the Hamilton-Jacobi equation for the geodesic Hamiltonian, a particular Hamiltonian function constructed from the metric of the spacetime that gives rise to the geodesic equation. In this scenario, the existence of classes of coordinate systems that separate the Hamilton-Jacobi equation, the so-called separability structures, turns out to be intimately connected to the existence of symmetries. In fact, this study leads to the most general form taken by the metric tensor in n dimensions containing m ≤ n rank-2 Killing tensors in involution with each other and r = n − m commuting Killing vector fields. The close relationship between the notion of separability structures and the existence of symmetries is manifest in this framework. In particular, we show that the existence of a separability structure enables the complete integrability of the geodesic motion. Then, a study on symmetries from the point of view of the action of continuous group on differential manifolds is conducted. A review on groups, Lie groups and Lie algebras is provided, and a study on spaces admitting the particular case of a separability structure with m = 2 is done under the light of these tools. Finally, equipped with all this knowledge, starting with the most general fourdimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. We assume that the gauge eld inherits the symmetries of the background and is aligned with the principal null directions of the spacetime. In particular, generalizations of the Kerr-NUT-(A)dS spacetime containing nonabelian gauge elds as source of matter are obtained.Nesta dissertação, simetrias são estudadas no contexto de relatividade geral. Inicialmente, tratamos do problema da separabilidade da equação de Hamilton-Jacobi para o hamiltoniano geodésico, uma função hamiltoniana específica, construída a partir da métrica do espaço-tempo, que dá origem à equação geodésica. Nesse cenário, a existência de classes de sistemas de coordenadas que separam a equação de Hamilton-Jacobi, as chamadas estruturas de separabilidade, estão intimamente conectadas à existência de simetrias. De fato, esse estudo nos leva à forma mais geral adotada pelo tensor métrico em n dimensões contendo m ≤ n tensores de Killing de rank 2 em involução entre si e r = n − m campos vetoriais de Killing que comutam entre si. A relação íntima entre a noção de estruturas de separabilidade com a existência de simetrias é evidente nesse cenário. Em particular, mostramos que a existência de uma estrutura de separabilidade permite a integrabilidade completa do movimento geodésico. Em seguida, um estudo de simetrias do ponto de vista da ação de um grupo contínuo em variedades diferenciáveis é conduzido. Uma revisão de grupos, grupos de Lie e álgebras de Lie é fornecido, e um estudo sobre espaços admitindo uma estrutura de separabilidade com m = 2 é feito sob luz desta abordagem. Então, munidos de todo esse conhecimento, partindo do espaço-tempo quadridimensional mais geral possuindo dois vetores de Killing que comutam entre si e um tensor de Killing não-trivial, integramos analiticamente as equações de Einstein-Yang-Mills para um grupo de calibre completamente arbitrário. Consideramos que os campos de calibre herdam as simetrias do espaço-tempo de fundo e estão alinhados com as direções principais nulas do espaço-tempo. Em particular, generalizações da solução de Kerr-NUT-(A)dS contendo campos de calibre não-abelianos como fontes de matéria são obtidas.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessSimetriasIntegrabilidadeTeoria de Einstein-Yang- MillsSoluções exatasOn symmetries of exact solutions of Einstein field equationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILDISSERTAÇÃO Gabriel Luz Almeida.pdf.jpgDISSERTAÇÃO Gabriel Luz Almeida.pdf.jpgGenerated Thumbnailimage/jpeg1296https://repositorio.ufpe.br/bitstream/123456789/34291/5/DISSERTA%c3%87%c3%83O%20Gabriel%20Luz%20Almeida.pdf.jpgf37a4e163296ebcb12a1d1e77ed3b039MD55ORIGINALDISSERTAÇÃO Gabriel Luz Almeida.pdfDISSERTAÇÃO Gabriel Luz Almeida.pdfapplication/pdf981071https://repositorio.ufpe.br/bitstream/123456789/34291/1/DISSERTA%c3%87%c3%83O%20Gabriel%20Luz%20Almeida.pdf1c2630dbc2efbb4e1233cc6da13933c4MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv On symmetries of exact solutions of Einstein field equations
title On symmetries of exact solutions of Einstein field equations
spellingShingle On symmetries of exact solutions of Einstein field equations
ALMEIDA, Gabriel Luz
Simetrias
Integrabilidade
Teoria de Einstein-Yang- Mills
Soluções exatas
title_short On symmetries of exact solutions of Einstein field equations
title_full On symmetries of exact solutions of Einstein field equations
title_fullStr On symmetries of exact solutions of Einstein field equations
title_full_unstemmed On symmetries of exact solutions of Einstein field equations
title_sort On symmetries of exact solutions of Einstein field equations
author ALMEIDA, Gabriel Luz
author_facet ALMEIDA, Gabriel Luz
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/4974855586479672
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/0760705959572749
dc.contributor.author.fl_str_mv ALMEIDA, Gabriel Luz
dc.contributor.advisor1.fl_str_mv SILVA FILHO, Carlos Alberto Batista da
contributor_str_mv SILVA FILHO, Carlos Alberto Batista da
dc.subject.por.fl_str_mv Simetrias
Integrabilidade
Teoria de Einstein-Yang- Mills
Soluções exatas
topic Simetrias
Integrabilidade
Teoria de Einstein-Yang- Mills
Soluções exatas
description SILVA FILHO, Carlos Alberto Batista da, também é conhecido em citações bibliográficas por: BATISTA, Carlos
publishDate 2019
dc.date.accessioned.fl_str_mv 2019-10-08T17:06:27Z
dc.date.available.fl_str_mv 2019-10-08T17:06:27Z
dc.date.issued.fl_str_mv 2019-06-27
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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identifier_str_mv ark:/64986/0013000014t71
dc.language.iso.fl_str_mv eng
language eng
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rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
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dc.publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.publisher.program.fl_str_mv Programa de Pos Graduacao em Fisica
dc.publisher.initials.fl_str_mv UFPE
dc.publisher.country.fl_str_mv Brasil
publisher.none.fl_str_mv Universidade Federal de Pernambuco
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reponame_str Repositório Institucional da UFPE
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