Universo tipo-Gödel em teorias de gravitação modificada

Abstract

The most recent findings indicate that the universe is undergoing accelerated expansion, which raises the need to reexamine the structure of General Relativity. In response to this challenge, several modified gravitational theories are emerging, and this thesis addresses five of them: Palatini f(R, T) Gravity, Hybrid Palatini f(R, T) Gravity, f(R, T, RµνT µν) Gravity, f(R, ϕ, X) Gravity, and f(R, Lm, T) Gravity. In this context, a primary focus of investigation is the causality problem, which is explored using the metric originally proposed by Kurt G¨odel, as well as a variation known as the G¨odel-type metric. Our analyses reveal that, when considering each of the modified gravitational theories and employing perfect fluid as the content of matter, we obtain non-causal solutions. These solutions exhibit regions where closed timelike curves are possible, which raises fundamental questions about causality within the framework of these theories. To address this issue and find causal solutions, we explore different forms of matter content, including scalar fields, electromagnetic fields, and combinations thereof. In conclusion, this study successfully identifies causal solutions for each of the considered modified gravitational theories, paving the way for a deeper understanding of causality within these theories and their implications for the structure of the universe.