Dinâmica relativística de partículas em torno de objetos ultracompactos

• Ano de defesa: 2019
• Autor(a) principal: Klën, Wayner de Souza
• Orientador(a): Molina, Carlos
• Banca de defesa: Saa, Alberto , Caldas, Iberê Luiz , Hase, Masayuki Oka
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• dARK ID: ark:/80033/0013000001xrk
• Idioma: por
• Instituição de defesa: Universidade de São Paulo - USP
• Programa de Pós-Graduação: Programa de Pós graduação em Modelagem de Sistemas Complexos
• Departamento: Escola de Artes, Ciências e Humanidades
• País: Brasil
• Palavras-chave em Português: Buracos negros; Sistemas dinâmicos; Estabilidade de Lypunov; Estabilidade de Jacobi; Bifurcação de Bogdanov-Takens
• Área do conhecimento CNPq: Ciências Exatas e da Terra; Física; Relatividade e Gravitação
• Link de acesso: https://deposita.ibict.br/handle/deposita/627

In this dissertation, the problem associated with the stability of timelike and null geodesics is studied from the dynamical system point of view. A succinct bibliographical review covering important aspects of time-continuous dynamical systems is made, and a short review about some topics of interest of general relativity is also presented. The geodesic equations of motion are shown for geometries with spherical symmetry, and the Schwarzschild case is first analyzed. In the following, we analyze the geometries proposed by Casadio, Fabbri, and Mazzacurati and an asymptotically de Sitter wormhole case. The characterization of the fixed points of the system is performed, and their stability is studied from the perspective of the Lyapunov and Jacobi methods, as well as the bifurcation analysis. The photon sphere is characterized as a limit cycle, being a strictly unstable fixed point in the state space of the system. The wormhole analysis reveals the existence of a stable photon sphere in certain regions of the parameter space of the system.