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

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.