On the causality properties in non-local gravity theories

TL;DR

This paper investigates the consistency of G"odel-type metrics in non-local gravity theories, finding exact solutions and analyzing their properties within a ghost-free, classical framework.

Contribution

It provides the first analysis of G"odel-type solutions in non-local gravity, identifying exact solutions for specific classes within the theory.

Findings

Found exact solutions for degenerate and hyperbolic G"odel-type metrics.

Demonstrated the ghost-free nature of the non-local models considered.

Analyzed the classical solutions' properties within the non-local gravity framework.

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 G\"{o}del-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 exactly solutions for the field equations correspondent to the degenerate ($\omega=0$) and hyperbolic ($m^{2}=4\omega^2$) classes of ST-homogeneous G\"{o}del-type metrics.