Conformally-flat, non-singular static metric in infinite derivative gravity

TL;DR

This paper demonstrates that in infinite derivative gravity, the Schwarzschild solution becomes conformally-flat and non-singular, potentially replacing black holes with smooth, horizonless objects due to non-local effects that smear out singularities.

Contribution

It shows that infinite derivative gravity modifies the Schwarzschild solution, removing singularities and horizons, and suggests a new class of non-singular compact objects governed by non-locality.

Findings

Schwarzschild metric does not satisfy boundary conditions at the origin in infinite derivative gravity.

Spacetime becomes conformally-flat and free of singularities within the non-local region.

Gravity remains weak across all scales, with potential implications for black hole physics.

Abstract

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.