Palatini formulation of non-local gravity

TL;DR

This paper derives the equations for a non-local gravity model using the Palatini formalism and finds that it does not eliminate singularities in vacuum solutions, aligning with general relativity in some cases.

Contribution

It introduces a Palatini-based formulation of non-local gravity and analyzes its properties and solutions, highlighting its similarities to Einstein's gravity in certain cases.

Findings

Vacuum solutions of GR are also solutions in the non-local model

Singularities are not removed in some cases of the non-local model

The model's properties are discussed within the Palatini formalism

Abstract

We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have shown that, in some specific cases, the vacuum solutions of general relativity are also vacuum solutions of the non-local model, so we conclude that, at least in this case, the singularities of Einstein's gravity are not removed.