Exact solutions and spacetime singularities in nonlocal gravity

TL;DR

This paper presents exact classical solutions in nonlocal gravity theories, including well-known spacetimes like Schwarzschild and FRW, and discusses potential resolutions of singularities through conformal invariance and delocalization.

Contribution

It provides explicit exact solutions for a broad class of weakly nonlocal gravity theories, extending known solutions to higher dimensions and different spacetime geometries.

Findings

Flat and Ricci-flat spacetimes are solutions.

Schwarzschild, Kerr, and (Anti-) de Sitter solutions are valid.

FRW solutions with conformal matter are obtained.

Abstract

We give here a list of exact classical solutions of a large class of weakly nonlocal theories of gravity, which are unitary and super-renormalizable (or finite) at quantum level. It is explicitly shown that flat and Ricci-flat spacetimes as well as maximally symmetric manifolds are exact solutions of the equation of motion. Therefore, well-known physical spacetimes like Schwarzschild, Kerr, (Anti-) de Sitter serve as solutions for standard matter content. In dimension higher than four we can also have Anti-de Sitter solutions in the presence of positive cosmological constant. We pedagogically show how to obtain these exact solutions. Furthermore, for another version of the theory, written in the Weyl basis, Friedmann-Robertson-Walker (FRW) spacetimes are also exact solutions, when the matter content is given by conformal matter (radiation). We also comment on the presence of singularities and possible resolution of them in finite and conformally invariant theories. "Delocalization" is proposed as a way to solve the black hole singularity problem. In order to solve the problem of cosmological singularities it seems crucial to have a conformally invariant or asymptotically free quantum gravitational theory.