Teorias modificadas da gravitação e a violação de causalidade

Abstract

In this thesis we deal with G odel-type Universes in the context of modi ed gravity, in particular, Chern-Simons modi ed gravity and Brans-Dicke theory with cosmological constant (BD- ). The G odel-type metrics have been intensively discussed in the General Relativity (GR) over years. It is known that such a metrics present Closed Time-like Curves (CTC's), in other words, the G odel-type metrics are themselves an example of the causality violation. Our goal is verify the consistency of the G odel-type metrics within the Chern-Simons modi ed gravity in both: non-dynamical and dynamical formulations. In the non-dynamical framework, we show that is possible a vacuum solution in contrast to GR. Another essentially new result that we get is the presence of causal solutions for a well-motivated matter source, in general, the solutions have no analogue in GR. Moreover, the vacuum solution represents the limiting case separating the completely causal and non-causal regions, such a property re ects the topological features of the Chern-Simons theory. The primordial distinguishing feature between the Chern-Simons modi ed gravity and GR solutions is the presence of the breaking Lorentz symmetry. It turns out this breaking opens up a range of new solutions. We show that the non-trivial Chern-Simons solutions in the non-dynamical framework is accompanied by rst-order corrections of the Lorentz-violating parameter. Furthermore, in the dynamical framework the geometric parameters are also a ected by second-order corrections of the Lorentzviolating parameter. We also investigated the G odel-type metrics in BD- model. We obtain a vacuum solution which is completely causal, m2 = 4!2, where for ~! ! 1 one recovers the GR with a scalar eld and cosmological constant. It is worth calling attention to the role of the cosmological constant that is fundamental in this context.