Gödel-type universes in energy–momentum-squared gravity

In this paper, a modification of general relativity is considered. It consists of generalizing the Lagrangian of matter in a non-linear way, that is, replacing the curvature scalar R by a function f ( R , T μ ν T μ ν ) , where T μ ν is the energy–momentum tensor. The main objective is to investigate the issue of causality in this gravitational model. To study the causality and/or its violation the Gödel-type solutions are used. For such development, different matter contents are chosen. A critical radius, beyond which causality is violated, is calculated. It is shown that both causal and non-causal solutions are allowed.