G\"{o}del-type solution in $f(R,T)$ modified gravity

TL;DR

This paper investigates causality violations in $f(R,T)$ modified gravity, analyzing scenarios with perfect fluid and scalar field matter content to understand the conditions under which causality may be violated.

Contribution

It provides a detailed analysis of causality issues in $f(R,T)$ gravity considering different matter configurations, which is a novel exploration in this modified gravity framework.

Findings

Causality violation depends on matter content and specific $f(R,T)$ models.

Perfect fluid alone may not lead to causality issues.

Scalar field inclusion influences causality conditions.

Abstract

In this paper, we will examine the problem of violation of causality in $f(R,T)$ modified gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor $T_{\mu\nu}$. We investigate the causality problem in two special cases, in the first we consider the matter content of the universe as a perfect fluid and in the second case, the matter content is a perfect fluid plus a scalar field.