Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UFPB |
Texto Completo: | https://repositorio.ufpb.br/jspui/handle/123456789/29944 |
Resumo: | The presente dissertation delas with comparisons between two approaches for energyand Momentum of the gravitational field, namely, the Landau-Lifshitz pseudotensor and the energy-momentum tensor of teleparallelism. The problem of determining gravitational energy dates back to the emergence of general relativity in 1915. It is a problem of great importance for Physics, since the concepts of energy and momentum are fundamental both for classical theories and quantum mechanics. Understanding how the gravitational field behaves is fundamental to solving one of the biggest problems in modern physics, the con- struction of a quantum theory of gravitation; certainly, there solution of the gravitational field energy problem will help in this understanding. Due to the numerous approaches to solve this problem, it was not possible to make a detailed description of each one. Thus, we decided to work with only the Landau-Lifshitz pseudotensor and the telepar- allelism tensor. The Landau-Lifshitz pseudotensor is defined in the contexto of general relativity and is often used in textbooks when one wants to give a qualitative description of the gravitational field energy. The teleparallelism tensor we used was developed in the context of a theory that provides the same field equations as GR but has a notion of dis- tant parallelism; this theory is known as Teleparallelism Equivalent to General Relativity (TEGR). In this dissertation, we presente results that show that the teleparallelism tensor presentes more adequate properties to describe the gravitational field than the Landau- Lifshitz pseudotensor. We discuss, for example, the result that is already well known in the literature that the teleparallel version reproduces the equation of state of a massless field, while the Landau-Lifshitz pseudotensor is not always capable of such a feat.As an original result, we were able to show that for a weak field and with a suitable “gauge” choice the Landau-Lifshitz pseudotensor differs from the teleparallel one by a fourth order term. We also made exact comparisons in the spacetime of plane waves, known generically as pp-waves. |
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Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismoGravidadeEspaço-tempoCurvaturaTeleparalelismoPseudotensorEnergia do campo gravitacionalGravitySpace-timeCurvatureTeleparallelismEnergy-momentumCNPQ::CIENCIAS EXATAS E DA TERRA::FISICAThe presente dissertation delas with comparisons between two approaches for energyand Momentum of the gravitational field, namely, the Landau-Lifshitz pseudotensor and the energy-momentum tensor of teleparallelism. The problem of determining gravitational energy dates back to the emergence of general relativity in 1915. It is a problem of great importance for Physics, since the concepts of energy and momentum are fundamental both for classical theories and quantum mechanics. Understanding how the gravitational field behaves is fundamental to solving one of the biggest problems in modern physics, the con- struction of a quantum theory of gravitation; certainly, there solution of the gravitational field energy problem will help in this understanding. Due to the numerous approaches to solve this problem, it was not possible to make a detailed description of each one. Thus, we decided to work with only the Landau-Lifshitz pseudotensor and the telepar- allelism tensor. The Landau-Lifshitz pseudotensor is defined in the contexto of general relativity and is often used in textbooks when one wants to give a qualitative description of the gravitational field energy. The teleparallelism tensor we used was developed in the context of a theory that provides the same field equations as GR but has a notion of dis- tant parallelism; this theory is known as Teleparallelism Equivalent to General Relativity (TEGR). In this dissertation, we presente results that show that the teleparallelism tensor presentes more adequate properties to describe the gravitational field than the Landau- Lifshitz pseudotensor. We discuss, for example, the result that is already well known in the literature that the teleparallel version reproduces the equation of state of a massless field, while the Landau-Lifshitz pseudotensor is not always capable of such a feat.As an original result, we were able to show that for a weak field and with a suitable “gauge” choice the Landau-Lifshitz pseudotensor differs from the teleparallel one by a fourth order term. We also made exact comparisons in the spacetime of plane waves, known generically as pp-waves.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESA presente dissertação versa sobre comparações entre duas abordagens para energia e o Momento do campo gravitacional, a saber, o pseudotensor de Landau-Lifshitz e o tensor de energia-momento do teleparalelismo. O problema da determinação da energia gravi- tacional vem desde do surgimento da relatividade geral (RG), em 1915. Trata-se de um problema de grande importância para a Física, uma vez que os conceitos de energia e mo- mento são fundamentais tanto para as teorias clássicas quanto para a mecânica quântica. A compreensão de como o campo gravitacional se comporta é fundamental para resolver um dos maiores problemas da física moderna, a construção de uma teoria quântica da gra- vitação; certamente, a resolução do problema da energia do campo gravitacional ajudará nessa compreensão. Devido às inúmeras abordagens para solução desse problema, nãofoi possível fazer uma descrição detalhada de cada uma. Assim, decidimos trabalhar com apenas o pseudotensor de Landau-Lifshitz e o tensor do teleparalelismo. O pseudotensor de Landau-Lifshitz é definido no contexto da RG e é frequentemente usado em livros tex- tos quando se deseja dar uma descrição qualitativa da energia do campo gravitacional. Já o tensor do Teleparalelismo que usamos foi desenvolvido no contexto de uma teoria que fornece as mesmas equações de campo da RG porém possui uma noção de paralelismo distante; essa teoria é conhecida como Teleparalelismo Equivalente à Relatividade Geral (TEGR). Nesta dissertação, apresentamos resultados que mostram que o tensor do tele- paralelismo apresenta propriedades mais adequadas para descrever o campo gravitacional que o pseudotensor de Landau-Lifshitz. Discutimos, por exemplo, o resultado que já é bem conhecido na literatura de que a versão teleparalela reproduza equação de estado de um campo sem massa, enquanto que o pseudotensor de Landau-Lifshitz nem sempre é capaz de tal feito. Como resultado original, fomos capazes demostrar que para um campo fraco e com um escolha adequadado “gauge” o pseudotensor de Landau-Lifshitz difere do teleparalelo por um termo de quarta ordem.Também fizemos comparações exatas no espaço-tempo de ondas planas, conhecido genericamente por pp-waves.Universidade Federal da ParaíbaBrasilFísicaPrograma de Pós-Graduação em FísicaUFPBFormiga, Jansen Brasileirohttp://lattes.cnpq.br/1666058727081809Andrade, João Leno Santos de2024-04-02T11:01:46Z2023-08-252024-04-02T11:01:46Z2023-07-28info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttps://repositorio.ufpb.br/jspui/handle/123456789/29944porAttribution-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nd/3.0/br/info:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFPBinstname:Universidade Federal da Paraíba (UFPB)instacron:UFPB2024-04-03T06:03:43Zoai:repositorio.ufpb.br:123456789/29944Biblioteca Digital de Teses e Dissertaçõeshttps://repositorio.ufpb.br/PUBhttp://tede.biblioteca.ufpb.br:8080/oai/requestdiretoria@ufpb.br|| diretoria@ufpb.bropendoar:2024-04-03T06:03:43Biblioteca Digital de Teses e Dissertações da UFPB - Universidade Federal da Paraíba (UFPB)false |
dc.title.none.fl_str_mv |
Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo |
title |
Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo |
spellingShingle |
Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo Andrade, João Leno Santos de Gravidade Espaço-tempo Curvatura Teleparalelismo Pseudotensor Energia do campo gravitacional Gravity Space-time Curvature Teleparallelism Energy-momentum CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo |
title_full |
Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo |
title_fullStr |
Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo |
title_full_unstemmed |
Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo |
title_sort |
Comparando o pseudotensor de Landau-Lifshitz com o tensor de energia-momento do teleparalelismo |
author |
Andrade, João Leno Santos de |
author_facet |
Andrade, João Leno Santos de |
author_role |
author |
dc.contributor.none.fl_str_mv |
Formiga, Jansen Brasileiro http://lattes.cnpq.br/1666058727081809 |
dc.contributor.author.fl_str_mv |
Andrade, João Leno Santos de |
dc.subject.por.fl_str_mv |
Gravidade Espaço-tempo Curvatura Teleparalelismo Pseudotensor Energia do campo gravitacional Gravity Space-time Curvature Teleparallelism Energy-momentum CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
topic |
Gravidade Espaço-tempo Curvatura Teleparalelismo Pseudotensor Energia do campo gravitacional Gravity Space-time Curvature Teleparallelism Energy-momentum CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
description |
The presente dissertation delas with comparisons between two approaches for energyand Momentum of the gravitational field, namely, the Landau-Lifshitz pseudotensor and the energy-momentum tensor of teleparallelism. The problem of determining gravitational energy dates back to the emergence of general relativity in 1915. It is a problem of great importance for Physics, since the concepts of energy and momentum are fundamental both for classical theories and quantum mechanics. Understanding how the gravitational field behaves is fundamental to solving one of the biggest problems in modern physics, the con- struction of a quantum theory of gravitation; certainly, there solution of the gravitational field energy problem will help in this understanding. Due to the numerous approaches to solve this problem, it was not possible to make a detailed description of each one. Thus, we decided to work with only the Landau-Lifshitz pseudotensor and the telepar- allelism tensor. The Landau-Lifshitz pseudotensor is defined in the contexto of general relativity and is often used in textbooks when one wants to give a qualitative description of the gravitational field energy. The teleparallelism tensor we used was developed in the context of a theory that provides the same field equations as GR but has a notion of dis- tant parallelism; this theory is known as Teleparallelism Equivalent to General Relativity (TEGR). In this dissertation, we presente results that show that the teleparallelism tensor presentes more adequate properties to describe the gravitational field than the Landau- Lifshitz pseudotensor. We discuss, for example, the result that is already well known in the literature that the teleparallel version reproduces the equation of state of a massless field, while the Landau-Lifshitz pseudotensor is not always capable of such a feat.As an original result, we were able to show that for a weak field and with a suitable “gauge” choice the Landau-Lifshitz pseudotensor differs from the teleparallel one by a fourth order term. We also made exact comparisons in the spacetime of plane waves, known generically as pp-waves. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-08-25 2023-07-28 2024-04-02T11:01:46Z 2024-04-02T11:01:46Z |
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://repositorio.ufpb.br/jspui/handle/123456789/29944 |
url |
https://repositorio.ufpb.br/jspui/handle/123456789/29944 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
Attribution-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal da Paraíba Brasil Física Programa de Pós-Graduação em Física UFPB |
publisher.none.fl_str_mv |
Universidade Federal da Paraíba Brasil Física Programa de Pós-Graduação em Física UFPB |
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reponame:Biblioteca Digital de Teses e Dissertações da UFPB instname:Universidade Federal da Paraíba (UFPB) instacron:UFPB |
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Universidade Federal da Paraíba (UFPB) |
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UFPB |
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UFPB |
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Biblioteca Digital de Teses e Dissertações da UFPB |
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Biblioteca Digital de Teses e Dissertações da UFPB |
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Biblioteca Digital de Teses e Dissertações da UFPB - Universidade Federal da Paraíba (UFPB) |
repository.mail.fl_str_mv |
diretoria@ufpb.br|| diretoria@ufpb.br |
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1801843031372988416 |