Infinite derivative gravity resolves nonscalar curvature singularities

TL;DR

This paper demonstrates that infinite derivative gravity (IDG), a nonlocal modification of general relativity, effectively resolves nonscalar curvature singularities in exact gravitational wave solutions, unlike standard GR.

Contribution

The study provides explicit examples showing IDG removes nonscalar curvature singularities in pp-wave solutions, advancing understanding of nonlocal gravity theories.

Findings

IDG solutions have finite curvature at singular points.

GR solutions exhibit nonscalar curvature singularities.

IDG modifies gravitational wave solutions to be nonsingular.

Abstract

We explicitly demonstrate that the nonlocal ghost-free ultraviolet modification of general relativity (GR) known as the infinite derivative gravity (IDG) resolves nonscalar curvature singularities in exact solutions of the full theory. We analyze exact pp-wave solutions of GR and IDG describing gravitational waves generated by null radiation. Curvature of GR and IDG solutions with the same energy-momentum tensor is compared in parallel-propagated frames along timelike and null geodesics at finite values of the affine parameter. While the GR pp-wave solution contains a physically problematic nonscalar curvature singularity at the location of the source, the curvature of its IDG counterpart is finite.