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

Abstract

In this work, we scrutinize the consistency of spacetime homogeneous Gödel-type metrics within f(R, Q, P) theories of gravity for well-motivated matter sources. As it is well known, such geometries allow for causality violation. We provide general conditions to engender completely causal solutions in a manner completely different from general relativity. We take some specific models, for instance, f(R,Q,P)=R -dfrac{mu ^{4n+2}}{left( a R^2+b Q+c Pright) ^n}, to illustrate the general results. Notably, we also find an unusual completely causal vacuum solution in the presence of a non-trivial cosmological constant which corresponds to the case m^2=4omega ^2.