A deflexão da luz e o Teorema de Gauss-Bonnet

Detalhes bibliográficos
Ano de defesa: 2019
Autor(a) principal: Carvalho, Icaro Daniel Dias de
Orientador(a): Carvalho, Ricardo Renan Landim de
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Relatividade Geral
Geometria diferencial
Teorema de Gauss-Bonnet
Link de acesso: http://www.repositorio.ufc.br/handle/riufc/44569
Resumo: This work aims to present a methodology for the calculation of the angle of light deflection caused by agravitational field. This methodology consists in using the generalized Fermat principle for a space-time with spherical and static symmetry and the Gauss-Bonnet theorem, associating the optical metric with the metric induced in a surface. We present the equations of the gravitational field, some solutions of the field equations and the generalization of the Fermat principle. Some essential definitions of differential geometry a represented and the Gauss-Bonnet theorem is developed. In this work it was possible to understand the focus of the light rays has a topological character, as shown by Gibbons and it was possible to present the methodology that allows to calculate the angle of light deflection that can be used for asymptotically flat spacetime and for non-asymptotically flat spacetime.
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spelling Carvalho, Icaro Daniel Dias deMendes, Wendel MacedoCarvalho, Ricardo Renan Landim de2019-08-07T19:57:16Z2019-08-07T19:57:16Z2019CARVALHO, I. D. D. A deflexão da luz e o teorema de Gauss-Bonnet. 2019. 79 f. Dissertação (Mestrado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2019.http://www.repositorio.ufc.br/handle/riufc/44569This work aims to present a methodology for the calculation of the angle of light deflection caused by agravitational field. This methodology consists in using the generalized Fermat principle for a space-time with spherical and static symmetry and the Gauss-Bonnet theorem, associating the optical metric with the metric induced in a surface. We present the equations of the gravitational field, some solutions of the field equations and the generalization of the Fermat principle. Some essential definitions of differential geometry a represented and the Gauss-Bonnet theorem is developed. In this work it was possible to understand the focus of the light rays has a topological character, as shown by Gibbons and it was possible to present the methodology that allows to calculate the angle of light deflection that can be used for asymptotically flat spacetime and for non-asymptotically flat spacetime.Este trabalho tem como objetivo apresentar uma metodologia de cálculo do ângulo de deflexão da luz causado por um campo gravitacional. Esta metodologia consiste em utilizar o princípio de Fermat generalizado para um espaço-tempo com simetria esférica e estático e o teorema de Gauss-Bonnet, associando a métrica óptica à métrica induzida em uma superfície. No primeiro momento são apresentadas as equações de campo gravitacional, algumas soluções das equações de campo e formulação generalizada do princípio de Fermat. Apresenta-se algumas definições essenciais sobre geometria diferencial e é desenvolvido o teorema de Gauss-Bonnet. Neste trabalho foi possível compreender que a focalização dos raios luminosos tem um caráter topológico, como mostrado por Gibbons e foi possível apresentar uma metodologia que possibilita calcular o ângulo de deflexão da luz tanto para espaços assintoticamente planos quanto não planos.Relatividade GeralGeometria diferencialTeorema de Gauss-BonnetA deflexão da luz e o Teorema de Gauss-Bonnetinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/44569/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52ORIGINAL2019_dis_iddcarvalho.pdf2019_dis_iddcarvalho.pdfapplication/pdf1131613http://repositorio.ufc.br/bitstream/riufc/44569/1/2019_dis_iddcarvalho.pdf28e322b01cf40f0e826c6156a88b4281MD51riufc/445692019-08-07 16:57:16.905oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2019-08-07T19:57:16Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv A deflexão da luz e o Teorema de Gauss-Bonnet
title A deflexão da luz e o Teorema de Gauss-Bonnet
spellingShingle A deflexão da luz e o Teorema de Gauss-Bonnet
Carvalho, Icaro Daniel Dias de
Relatividade Geral
Geometria diferencial
Teorema de Gauss-Bonnet
title_short A deflexão da luz e o Teorema de Gauss-Bonnet
title_full A deflexão da luz e o Teorema de Gauss-Bonnet
title_fullStr A deflexão da luz e o Teorema de Gauss-Bonnet
title_full_unstemmed A deflexão da luz e o Teorema de Gauss-Bonnet
title_sort A deflexão da luz e o Teorema de Gauss-Bonnet
author Carvalho, Icaro Daniel Dias de
author_facet Carvalho, Icaro Daniel Dias de
author_role author
dc.contributor.co-advisor.none.fl_str_mv Mendes, Wendel Macedo
dc.contributor.author.fl_str_mv Carvalho, Icaro Daniel Dias de
dc.contributor.advisor1.fl_str_mv Carvalho, Ricardo Renan Landim de
contributor_str_mv Carvalho, Ricardo Renan Landim de
dc.subject.por.fl_str_mv Relatividade Geral
Geometria diferencial
Teorema de Gauss-Bonnet
topic Relatividade Geral
Geometria diferencial
Teorema de Gauss-Bonnet
description This work aims to present a methodology for the calculation of the angle of light deflection caused by agravitational field. This methodology consists in using the generalized Fermat principle for a space-time with spherical and static symmetry and the Gauss-Bonnet theorem, associating the optical metric with the metric induced in a surface. We present the equations of the gravitational field, some solutions of the field equations and the generalization of the Fermat principle. Some essential definitions of differential geometry a represented and the Gauss-Bonnet theorem is developed. In this work it was possible to understand the focus of the light rays has a topological character, as shown by Gibbons and it was possible to present the methodology that allows to calculate the angle of light deflection that can be used for asymptotically flat spacetime and for non-asymptotically flat spacetime.
publishDate 2019
dc.date.accessioned.fl_str_mv 2019-08-07T19:57:16Z
dc.date.available.fl_str_mv 2019-08-07T19:57:16Z
dc.date.issued.fl_str_mv 2019
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.citation.fl_str_mv CARVALHO, I. D. D. A deflexão da luz e o teorema de Gauss-Bonnet. 2019. 79 f. Dissertação (Mestrado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2019.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufc.br/handle/riufc/44569
identifier_str_mv CARVALHO, I. D. D. A deflexão da luz e o teorema de Gauss-Bonnet. 2019. 79 f. Dissertação (Mestrado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2019.
url http://www.repositorio.ufc.br/handle/riufc/44569
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
instacron:UFC
instname_str Universidade Federal do Ceará (UFC)
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institution UFC
reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
bitstream.url.fl_str_mv http://repositorio.ufc.br/bitstream/riufc/44569/2/license.txt
http://repositorio.ufc.br/bitstream/riufc/44569/1/2019_dis_iddcarvalho.pdf
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repository.name.fl_str_mv Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)
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