Gödel-Type Universes in f(R) Gravity with an Arbitrary Coupling between Matter and Geometry

By studying the Gödel-type solution, the causality in f(R) gravity with an arbitrary coupling between matter and geometry is discussed. Assuming that the matter source is a perfect fluid and a scalar field, respectively, we find that for the perfect fluid case, noncausal Gödel−type solutions exist and there is a critical radius r_c beyond which the causality is violated. For the scalar field case, the violation of causality is forbidden.