Estudo das propriedades de buracos negros de Schwarzschild e de Kerr - Scarpin, Julia de Assis (Universidade Federal de São Carlos, 2022)
In this study, firstly General Relativity, defined by Albert Einstein in 1915, is introduced. In the first chapter, the concepts of geodesics and the Christoffel symbols are demonstrated, followed by a brief presentation of symmetries and conservation laws, those described by Killing vectors. After this, the Einstein equations are introduced, and how these are composed of curvature and the energy-momentum tensors. The following chapter presents the properties of a black hole described by the Schwarzschild metric, the trajectories followed by the geodesics in this metric, and the corresponding conformal diagrams. In addition, the ISCO (Innermost Stable Circular Orbit) parameters and a brief explanation of the metric singularities are given. The properties of rotating black holes are presented in Chapter 4. First, an introduction to the Kerr metric is made, followed by the exhibition of the two event horizons present in this metric and the singularities they possess. The understanding of such horizons can be acquired from three cases, which are also shown in this section. Next, the ergosphere and its definition are presented, as well as how particles behave at the ergosphere’s limit. In this chapter the ISCO parameters are also evidenced, now, however, for a rotating black hole. There is also a brief description of the idea behind the Penrose process, which stands for the theoretical energy extraction from a rotating black hole from a particle’s decay.
Study of the properties of Schwarzschild and Kerr black holes
Keywords: Relatividade geral; Buracos negros; Métrica de Schwarzschild; Métrica de Kerr; Tensores; Geodésicas; General relativity; Black holes; Schwarzschild metric; Kerr metric; Tensors; Geodesics; CIENCIAS EXATAS E DA TERRA::FISICA::FISICA GERAL::RELATIVIDADE E GRAVITACAO