Violação de causalidade em gravidade modificada f(R, T²)

Abstract

The discovery of the accelerated expansion of the universe has spurred studies proposing alternative models to Einstein’s general theory of relativity. This is because Einstein’s theory, without the inclusion of exotic components, fails to provide a consistent explanation for this acceleration. While many generalizations of the general theory of relativity focus on extending the gravitational Lagrangian by replacing the curvature scalar R of the Einstein-Hilbert Lagrangian with a function f(R), there is another generalization that involves the matter Lagrangian, which is nonlinear and replaces the function f(R) with a function f(R, TµνT µν), where Tµν representsthe energy-momentum tensor describing the matter content of the universe. The objective of this work is to investigate the issue of causality in this gravitational model, incorporating the effects of higher-order terms of the energy-momentum tensor into the gravitational Lagrangian. To achieve this, we will analyze the Godel and type-Godel solutions. The type-Godel metric is a generalization of the solution proposed by Kurt Godel in 1949, characterized by the presence of Closed Timelike Curves (CTCs), which lead to a violation of causality. It is important to note that this violation of causality does not occur locally, as the causal structure of spacetimes in general relativity is consistent with special relativity. However, on a non-local scale, significant differences can arise. The analysis of gravity described by the theory f(R, TµνTµν) reveals that, in its metric version, it results in a universe with a violation of causality for the original Godel solution. When we use the type-Godel metric together with a matter content consisting of a perfect fluid, we observe that gravity f(R, TµνT µν) once again leads to a non-causal universe. However, this time we find a finite critical radius beyond which causality is broken. By solving the field equations of gravity f(R, TµνT µν), considering both the perfect fluid and the scalar field as matter content, we obtain a solution in which the violation of causality does not occur spontaneously. Additionally, we observe that the scalar field is coupled to the derivative of the function f with respect to the square of the energy-momentum tensor. We also identify another solution in which only the scalar field acts as the matter content, resulting in a spontaneous causal relation. Therefore, we highlight the significant role played by the scalar field in gravity f(R, TµνTµν), as in the cases of f(R) andf(R, T) gravities, as it preserves the causal nature of the universe.