Defeitos topológicos em teorias modificadas da gravitação: soluções clássicas e modos quasinormais

Abstract

Recent observations seemed to indicate that the rate of the expansion of the universe is accelerating. Such observation, along with the fact that only approximately 5% of its content is composed of barionic matter, suggests that it is necessary to modify general relativity, in order to explain this acceleration. In this thesis, we study some wellknown proprosal for such endeavour, such as f(R) theories of gravity, Brans-Dicke theory and Lovelock theories. These models are studied in three subjects, namelly: The relation between these theories, in particular, the correspondence between Brans-Dicke and f(R) theories; classical gravitating solutions involving cosmic strings; and the quasinormal modes of black holes, in composition with topological defects (cosmic strings and monopoles). The classical solutions are studied numerically, and the astrophysical and cosmological effects due to the defect are analyzed. We found that, for a specific class of f(R) theories, such as f(R) = R - 2 + R2 + Rm, with m > 2, the angular deficit generated by the defect is attenuated, and the attenuation increases as the value of m decreases. In the context of quasinormal modes, we calculate the spectrum of quasinormal modes of a black hole, with a global monopole, in f(R) theories. After that, we study how this spectrum differs from the same system in general relativity. We also calculate the spectrum of a black hole, with a cloud of strings, in Lovelock gravity. After that we study how this spectrum differs from the spectrum of the same system, without the clound of strings. Also, we compare it with the same system, with a cloud of strings, but now in general relativity.