Alguns aspectos das teorias modificadas da gravitação via formalismo de Palatini

Abstract

Although Einstein’s theory of General Relativity has successfully passed for the classical tests along the time. Increasingly accurate measurements of temperature variations in cosmic background radiation and research involving galaxies and galaxy clusters have been shown a series of phenomena that have not yet been explained by the general theory of relativity; among them, we can mention the most paradigmatic of them: the accelerated expansion of the universe and the unexpected curve of galaxy rotation. In addition, Penrose and Hawking showed that for specific kinds of matter sources, the theory predicts geodesic singularities. At the singularity, General Relativity breaks down, namely, the theory is not valid at this level because one cannot take physical measurements since the geometrical quantities blow up at the singularity. On the face of these problems, the natural question comes up: can we formulate a theory of gravity capable of avoiding the singularities, explain the cosmological observations and, within the appropriate limit, reduces to the theory of General Relativity? In fact, there has been many proposals. In this thesis, we will explore two of them: a f(R) theory of gravity and Born-Infeld gravity. We will restrict our analysis to these models in metric-affine approach, also called Palatini formalism. In this formulation, the connection is, a priori, independent of the metric, in contrast to the metric formalism, where the connection depends on the metric components. In an alternative theory of gravity, in general, these two formulations are not equivalent. In the absence of matter, the two models we are going to deal with reduce to General Relativity plus an effective cosmological constant, so we need matter sources to get new solutions. In this perspective, we will couple the energy-moment tensor of the global monopole and of a non-linear sigma model to modified gravity. We will obtain very interesting solutions and very different from those provided by General Relativity. Among them, we highlight geodesically complete solutions, that is, without singularities, such as regular black holes and traversable wormholes.