Gödel metrics with chronology protection in Horndeski gravities

Abstract

Gödel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the Gödel-type metrics with chronology protection can emerge in Einstein–Horndeski gravity. We construct such exact solutions also in Einstein–Horndeski–Maxwell and Einstein–Horndeski–Proca theories.