G\"{o}del-type solutions within the $f(R,Q,P)$ gravity

TL;DR

This paper investigates G"{o}del-type solutions in $f(R,Q,P)$ gravity, identifying conditions for causality and presenting specific models with causal solutions, including a unique vacuum case with a cosmological constant.

Contribution

It provides new criteria for causality in G"{o}del-type metrics within $f(R,Q,P)$ gravity, expanding understanding beyond general relativity and exploring specific models and solutions.

Findings

Conditions for causal G"{o}del-type solutions in $f(R,Q,P)$ gravity

Existence of a unique causal vacuum solution with cosmological constant

Illustration of results with specific $f(R,Q,P)$ models

Abstract

In this work, we scrutinize the consistency of spacetime homogeneous G\"{o}del-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, $f(R,Q,P)=R -\dfrac{\mu^{4n+2}}{\left(a R^2+b Q+c P\right)^n}$, 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 $m^2=4\omega^2$.