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, $f(R,Q,P)=R-\frac{{\mu }^{4n+2}}{{\left(a{R}^2+bQ+cP\right)}^n}$, 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 $m^2=4{\omega }^2$.

18 pages, matches published version

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