Conserved quantities for spinning test particles in general relativity

Detalhes bibliográficos
Autor(a) principal: SANTOS, Esdras Barbosa dos
Data de Publicação: 2020
Tipo de documento: Tese
Idioma: por
Título da fonte: Repositório Institucional da UFPE
dARK ID: ark:/64986/0013000012z3s
Texto Completo: https://repositorio.ufpe.br/handle/123456789/38776
Resumo: SILVA FILHO, Carlos Alberto Batista da, também é conhecido em citações bibliográficas por: BATISTA, Carlos
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spelling SANTOS, Esdras Barbosa doshttp://lattes.cnpq.br/8037771277128864http://lattes.cnpq.br/0760705959572749SILVA FILHO, Carlos Alberto Batista da2020-11-25T20:03:49Z2020-11-25T20:03:49Z2020-08-28SANTOS, Esdras Barbosa dos. Conserved quantities for spinning test particles in general relativity. 2020. Tese (Doutorado em Física) - Universidade Federal de Pernambuco, Recife, 2020.https://repositorio.ufpe.br/handle/123456789/38776ark:/64986/0013000012z3sSILVA FILHO, Carlos Alberto Batista da, também é conhecido em citações bibliográficas por: BATISTA, CarlosIn 1937, Myron Mathisson initiated a research program with the aim of describing extended bodies in General Relativity, similar to what is done with rigid bodies in Classical Mechanics. In his theory, the internal structure of the bodies is described by using the so-called multipolar moments. When considering the spin of the particle beyond its translational motion, the motion of the particle is not necessarily geodesic anymore, being described by the so-called Mathisson-Papapetrou-Dixon (MPD) equations. In the early 1980s, R. Rudiger published two articles dedicated to study the most general conserved charges associated to the motion of particles with spin moving in a curved spacetime and described by the MPD equations. In particular, it was shown that, besides the well-known conserved quantity associated to Killing vectors, there is also another conserved quantity that is linear in the spin of the particle and which involves a Killing-Yano tensor. It was also shown in these papers that in order of this new scalar to be conserved, two obscure conditions involving the Killing-Yano tensor and the curvature tensor must be satisfied. In this thesis, we seek to shed light over these conditions, by trying delimitate the possible spacetimes in which these conditions are satisfied, i.e. in which this new conserved quantity is allowed to exist. In order to extract the content of the Rudiger conditions, some essential mathematical tools are introduced along the text. In this sense, we discuss about the so-called integrability conditions for the Killing-Yano tensors and also we introduce the Petrov classification, which is an important algebraic classification for the Weyl tensor valid in four-dimensional spacetimes. However, before discuss these tools, a revision concerning Mathisson’s theory and the MPD equations is made.CAPESEm 1937, Myron Mathisson iniciou um programa de pesquisa com a finalidade de descrever corpos extensos em Relatividade Geral, de uma forma semelhante ao que é feito com corpos rígidos em Mecânica Clássica. Em sua teoria, a estrutura interna dos corpos é descrita através dos chamados momentos multipolares. Quando consideramos o spin da partícula além do seu movimento translacional, o movimento da partícula não é mais necessariamente geodésico, e passa a ser descrito pelas chamadas equações de Mathisson-Papapetrou-Dixon (MPD). No início da década de 1980, R. Rüdiger publicou dois artigos dedicados a estudar as cargas conservadas mais gerais associadas ao movimento de partículas com spin se movendo num espaço-tempo curvo e que são descritas pelas equações MPD. Em particular, foi mostrado que, além da bem conhecida quantidade conservada associada a vetores de Killing que essas partículas admitem, existe ainda uma outra quantidade conservada linear no spin da partícula e que envolve um tensor de Killing-Yano. Foi provado ainda nesses artigos que, para que esse novo escalar seja conservado, duas condições obscuras envolvendo o tensor de Killing-Yano e o tensor de curvatura devem ser satisfeitas. Nessa tese, buscamos esclarecer o conteúdo dessas duas condições, buscando delimitar os possíveis espaços-tempos em que essas condições são satisfeitas, isto é, em que a nova quantidade conservada é permitida existir. Com a finalidade de extrair o conteúdo das condições de Rüdiger, algumas ferramentas matemáticas essenciais são introduzidas ao longo do texto. Deste modo, discutimos sobre as chamadas condições de integrabilidade dos tensores de Killing-Yano e também introduzimos a classificação de Petrov, que é uma importante classificação algébrica para o tensor de Weyl válida em espaçostempos em quatro dimensões. Contudo, antes de discutirmos essas ferramentas, uma revisão a respeito da teoria do Mathisson e das equações MPD é feita.porUniversidade 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/openAccessFísica Teórica e ComputacionalCorpos extensosRelatividade GeralEquações de Mathisson-Papapetrou-DixonConserved quantities for spinning test particles in general relativityinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETEXTTESE Esdras Barbosa dos Santos.pdf.txtTESE Esdras Barbosa dos Santos.pdf.txtExtracted texttext/plain153693https://repositorio.ufpe.br/bitstream/123456789/38776/4/TESE%20Esdras%20Barbosa%20dos%20Santos.pdf.txte65d9728c7cc802b62b3a65d289d825cMD54THUMBNAILTESE Esdras Barbosa dos Santos.pdf.jpgTESE Esdras Barbosa dos Santos.pdf.jpgGenerated Thumbnailimage/jpeg1216https://repositorio.ufpe.br/bitstream/123456789/38776/5/TESE%20Esdras%20Barbosa%20dos%20Santos.pdf.jpg2dc8062789008007cf84b1d7c8bf938dMD55CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv Conserved quantities for spinning test particles in general relativity
title Conserved quantities for spinning test particles in general relativity
spellingShingle Conserved quantities for spinning test particles in general relativity
SANTOS, Esdras Barbosa dos
Física Teórica e Computacional
Corpos extensos
Relatividade Geral
Equações de Mathisson-Papapetrou-Dixon
title_short Conserved quantities for spinning test particles in general relativity
title_full Conserved quantities for spinning test particles in general relativity
title_fullStr Conserved quantities for spinning test particles in general relativity
title_full_unstemmed Conserved quantities for spinning test particles in general relativity
title_sort Conserved quantities for spinning test particles in general relativity
author SANTOS, Esdras Barbosa dos
author_facet SANTOS, Esdras Barbosa dos
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/8037771277128864
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/0760705959572749
dc.contributor.author.fl_str_mv SANTOS, Esdras Barbosa dos
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 Física Teórica e Computacional
Corpos extensos
Relatividade Geral
Equações de Mathisson-Papapetrou-Dixon
topic Física Teórica e Computacional
Corpos extensos
Relatividade Geral
Equações de Mathisson-Papapetrou-Dixon
description SILVA FILHO, Carlos Alberto Batista da, também é conhecido em citações bibliográficas por: BATISTA, Carlos
publishDate 2020
dc.date.accessioned.fl_str_mv 2020-11-25T20:03:49Z
dc.date.available.fl_str_mv 2020-11-25T20:03:49Z
dc.date.issued.fl_str_mv 2020-08-28
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
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dc.identifier.citation.fl_str_mv SANTOS, Esdras Barbosa dos. Conserved quantities for spinning test particles in general relativity. 2020. Tese (Doutorado em Física) - Universidade Federal de Pernambuco, Recife, 2020.
dc.identifier.uri.fl_str_mv https://repositorio.ufpe.br/handle/123456789/38776
dc.identifier.dark.fl_str_mv ark:/64986/0013000012z3s
identifier_str_mv SANTOS, Esdras Barbosa dos. Conserved quantities for spinning test particles in general relativity. 2020. Tese (Doutorado em Física) - Universidade Federal de Pernambuco, Recife, 2020.
ark:/64986/0013000012z3s
url https://repositorio.ufpe.br/handle/123456789/38776
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/
info:eu-repo/semantics/openAccess
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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
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFPE
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