Causal Gödel-type metrics in non-local gravity theories

Abstract

Abstract It is well known that non-local theories of gravity have been a flourish arena of studies for many reasons, for instance, the UV incompleteness of General Relativity (GR). In this paper we check the consistency of ST-homogeneous Gödel-type metrics within the non-local gravity framework. The non-local models considered here are ghost-free but not necessarily renormalizable since we focus on the classical solutions of the field equations. Furthermore, the non-locality is displayed in the action through transcendental entire functions of the d’Alembert operator $$\Box $$ □ that are mathematically represented by a power series of the $$\Box $$ □ operator. We find two exact solutions for the field equations correspondent to the degenerate ( $$\omega =0$$ ω = 0 ) and hyperbolic ( $$m^{2}=4\omega ^2$$ m 2 = 4 ω 2 ) classes of ST-homogeneous Gödel-type metrics.