Gödel-type solutions in hybrid metric-Palatini gravity

Instituto de Física, Universidade Federal de Mato Grosso - 78060-900, Cuiabá, Mato Grosso, Brazil

^(a) junior@fisica.ufmt.br
^(b) alesandroferreira@fisica.ufmt.br (corresponding author)

Received: 12 May 2021
Accepted: 30 June 2021

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 . Here, 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 Gödel-type solutions, which essentially lead to violation of causality. Considering physically well-motivated matter sources, causal and non-causal solutions are explored.