G\"{o}del and G\"{o}del-type solutions in the Palatini $f(R,T)$ gravity theory

TL;DR

This paper investigates G"{o}del and G"{o}del-type solutions within Palatini $f(R,T)$ gravity, analyzing causality violations and demonstrating that non-causal solutions can be avoided with suitable matter content.

Contribution

It explores the existence of G"{o}del-type solutions in Palatini $f(R,T)$ gravity and shows how causality violations can be prevented through matter configurations.

Findings

Non-causal solutions can be avoided in Palatini $f(R,T)$ gravity.

A critical radius for causality violation is calculated.

Different matter contents influence the presence of causality violations.

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\"{o}del and G\"{o}del-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.