Non-singular "Gauss'' black hole from non-locality

TL;DR

This paper introduces a non-locality-based mechanism to model non-singular black holes with a de Sitter core, eliminating the inner horizon and reproducing the mass gap phenomenon in non-local theories.

Contribution

It provides a physically motivated non-local model for non-singular black holes, avoiding inner horizon issues and capturing the mass gap in black hole formation.

Findings

The geometry features a de Sitter core and no inner horizon for generic parameters.

An outer horizon exists only above a critical mass, indicating a mass gap.

The solution approximates vacuum Einstein equations outside astrophysical black holes.

Abstract

Cutting out an infinite tube around $r=0$ formally removes the Schwarzschild singularity, but without a physical mechanism this procedure seems ad hoc and artificial. In this paper we provide justification for such a mechanism by means of non-locality. Motivated by the Gauss law we define a suitable radius variable as the inverse of a regular non-local potential, and use this variable to model a non-singular black hole. The resulting geometry has a de\,Sitter core, and for generic values of the regulator there is \emph{no inner horizon}, saving this model from potential issues via mass inflation. An \emph{outer} horizon only exists for masses above a critical threshold, thereby reproducing the conjectured ``mass gap'' for black holes in non-local theories. The geometry's density and pressure terms decrease exponentially, thereby rendering it an almost-exact vacuum solution of the Einstein equations outside of astrophysical black holes. Its thermodynamic properties resemble that of the Hayward black hole, with the notable exception that for critical mass the horizon radius is zero.