G\"{o}del-type solutions in hybrid metric-Palatini gravity

TL;DR

This paper explores G"{o}del-type solutions within hybrid metric-Palatini gravity, analyzing the conditions under which causality may be violated due to non-minimal matter-geometry coupling.

Contribution

It derives the modified Einstein equations in hybrid metric-Palatini gravity and investigates the existence of G"{o}del-type solutions, including causal and non-causal cases.

Findings

Existence of G"{o}del-type solutions in the theory

Conditions for causality violation identified

Both causal and non-causal solutions found

Abstract

In this paper, the hybrid metric-Palatini gravity is an approach to modified gravity in which is added to the usual Einstein-Hilbert action a supplementary term containing a Palatini-type correction of the form $f({\cal R},T)$. Here, ${\cal R}$ is the Palatini curvature scalar, which is constructed from an independent connection and $T$ is the trace of the energy-momentum tensor. This theory describes a non-minimal coupling between matter and geometry. The modified Einstein field equations in this hybrid metric-Palatini approach are obtained. Then, it is investigated whether this modified theory of gravity and its field equations allow G\"{o}del-type solutions, which essentially lead to violation of causality. Considering physically well-motivated matter sources, causal and non-causal solutions are explored.