Gödel-type solutions within the f ( R , Q ) gravity

In this paper, we deal with the f(R,Q) gravity whose action depends, besides of the scalar curvature R, on the higher-derivative invariant Q=RμνRμν. In order to compare this theory with the usual general relativity (GR), we verify the consistency of Gödel-type solutions within the f(R,Q) gravity and discuss the related causality issues are discussed. Explicitly, we show that in the f(R,Q) gravity there are new Gödel-type completely causal solutions having no analogue in the general relativity. In particular, a remarkable Gödel-type solution corresponding to the conformally flat space and maximally symmetric for physically well-motivated matter sources, with no necessity of cosmological constant, has been considered. We demonstrate that, in contrast to GR framework, f(R,Q) gravity supports new vacuum solutions with the requirement for the cosmological constant to be nonzero. Finally, causal solutions are obtained for a particular choice f(R,Q)=R+αR2+βQ.