Causal G\xf6del-type metrics in non-local gravity theories

J R Nascimento,P J Porfírio,A Yu Petrov

doi:10.1140/epjc/s10052-021-09640-5

J R Nascimento, P J Porfírio + Show 1 more

Open Access

https://doi.org/10.1140/epjc/s10052-021-09640-5

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

Highlights

Of the most promising ways to solve the problem of ghosts is based on the development of a nonlocal generalization for gravity which could guarantee renormalizability or even UV finiteness for a corresponding theory
We have investigated ST-homogeneous Gödel-type metrics within the non-local gravity theory (1)
Despite the highly non-linear form of field equations we have succeeded in engendering exact solutions for this model

Summary

Introduction

Some of the few papers dealing with other metrics within the nonlocal context are [27,28] where various solutions with a constant and vanishing scalar curvature, namely, the (anti)de Sitter, the simple Gödel one, and pp-waves, were considered (some studies of perturbed Schwarzschild metric in a special form of a nonlocal gravity action are presented in [29]). In this paper we consider a more generic nonlocal gravity involving the scalar curvature and contractions of Ricci and Weyl tensors, and a more broad class of metrics, that is, the Gödel-type metrics characterized by two constant parameters m and ω, and, depending on these parameters, displaying either causal or non-causal behavior. The Appendix is devoted to description of the boost-weight decomposition we use in the paper

Non-local gravity theory

Field equations

ST-homogeneous Gödel-type metrics

ST-homogeneous Gödel-type metrics within non-local gravity

Completely causal solutions in non-local gravity

Summary and conclusions