Causal Gödel-type metrics in non-local gravity theories

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 ($$\omega =0$$) and hyperbolic ($$m^{2}=4\omega ^2$$) classes of ST-homogeneous Gödel-type metrics