Godel-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 mu nu T mu nu), where T-mu nu is the energy-momentum tensor. The man objective is to investigate the issue of causality in this gravitational model. To study the causality and/or its violation the Godel-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.