Relatividade geral no espaço-tempo bidimensional e tridimensional
Data
2020-10-05
Autores
Jamaica, Juan David Fonseca [UNIFESP]
Orientadores
Dias, Marco André Ferreira [UNIFESP]
Tipo
Trabalho de conclusão de curso de especialização
Título da Revista
ISSN da Revista
Título de Volume
Resumo
Em este trabalho é desenvolvido uma explicação mais exaustiva e pedagógica do artigo: General relativity in two and threedimensional space-times (Peter Collas, 1997) que, embora seja
uma pesquisa muito completa e rigorosa, por razões de sínteses os aspetos físicos e matemáticos
são mencionados mas não esclarecidos com detalhe. O comportamento da relatividade geral em
um Espaço-Tempo bidimensional e tridimensional é o tópico central a discutir. Como resultado
no caso bidimensional, foi mostrado que a ausência da matéria é independente da curvatura intrínseca da geometria Espaço-Temporal. No caso tridimensional foi mostrado que: se o espaço
estiver vazio a geometria tem que ser plana; existe uma solução interior que corresponde a um
universo de De Sitter; distribuições de massa nita garantem uma anulação da pressão. Finalmente, o modelo cosmológico para um universo de poeira é caracterizado por uma expansão do
tipo Hubble que corresponde ao modelo de Milne.
In this work, it has been developed a more exhaustive and pedagogical explanation of the article: General relativity in two and threedimensional space-times (Peter Collas, 1997) which, although it is a very complete and rigorous research, for synthesis rations the physical and mathematical aspects are mentioned but not clari ed in detail. The behavior of general relativity in a two-dimensional and three-dimensional space-time is the central topic to be discussed. As a result in the two-dimensional case, it was shown that the absence of matter is independent of the intrinsic curvature of space-time geometry. In the three-dimensional case, it was shown that: if the space is empty, the geometry has to be at; there is an interior solution that corresponds to a De Sitter universe; nite mass distributions guarantee an elimination of pressure. Finally, the cosmological model for a dust universe is characterized by an expansion of the Hubble type that corresponds to Milne's model.
In this work, it has been developed a more exhaustive and pedagogical explanation of the article: General relativity in two and threedimensional space-times (Peter Collas, 1997) which, although it is a very complete and rigorous research, for synthesis rations the physical and mathematical aspects are mentioned but not clari ed in detail. The behavior of general relativity in a two-dimensional and three-dimensional space-time is the central topic to be discussed. As a result in the two-dimensional case, it was shown that the absence of matter is independent of the intrinsic curvature of space-time geometry. In the three-dimensional case, it was shown that: if the space is empty, the geometry has to be at; there is an interior solution that corresponds to a De Sitter universe; nite mass distributions guarantee an elimination of pressure. Finally, the cosmological model for a dust universe is characterized by an expansion of the Hubble type that corresponds to Milne's model.