G\"odel and G\"odel-type solutions in the Palatini f(R,T) gravity theory
Abstract
The Palatini f(R,T) gravity theory is considered. The standard Einstein-Hilbert action is replaced by an arbitrary function of the Ricci scalar R and of the trace T of the energy-momentum tensor. In the Palatini approach, the Ricci scalar is a function of the metric and the connection. These two quantities, metric and connection, are taken as independents variables. Then, it is examined whether Palatini f(R,T) gravity theory allows solutions in which lead to violation of causality. The G\"odel and G\"odel-type space-times are considered. In addition, a critical radius, which permits to examine limits for violation of causality, is calculated. It is shown that, for different matter contents, non-causal solutions can be avoided in this Palatini gravitational theory.