Modelo cosmológico Kantowski-Sachs com radiação e gás de Chaplygin

Abstract

This study seeks to solve Einstein’s equations for a model with the Kantowski-Sachs metric and for a Misner parameterized Kantowski-Sachs metric. Initially, the Einstein’s equations for the Kanotwski-Sachs metric were determined. In the first model, the content is a perfect fluid of radiation and the second one is a Chaplygin gas. Altough the radiation model has already been studied, we made a deeper review of its solutions. On the other side, the Chaplygin gas model corresponds to the original contribuition of this dissertation. Hence, we initiated by calculating energy-momentum tensors, Ricci and Riemann tensors and the Einstein equations for the Kantowski-Sachs metric. In order to better understand the Kantowski-Sachs universe, we investigated and discussed the calculation presented in the Kantowski-Sachs article for a model filled with dust, and Gron, for a model filled with cosmological constant. Thereafter, we presented the analysis for the solutions of these equations for the models with radiation and Chaplygin gas. Thereafter, we followed the same steps for the Misner parameterized Kantowski-Sachs metric with radiation and Chaplygin gas. We analyzed the behaviour of the average scale factor and the evolution of the anisotropy, and it was possible to notice that for an universe filled with Chaplygin gas, the anisotropy will vanish, leading to a universe ruled by the FRW metric.