Geodesically complete black holes

TL;DR

This paper investigates the possible non-singular geometries of black holes in theories beyond general relativity, revealing a limited set of regular solutions and a tradeoff between internal consistency and observational deviations.

Contribution

It provides a comprehensive classification of non-singular black hole geometries under spherical symmetry, highlighting the inherent limitations and observational implications of such models.

Findings

Limited set of regular geometries identified

Revealed a tradeoff between internal consistency and deviations from GR

Uncovered new possible non-singular black hole solutions

Abstract

The 1965 Penrose singularity theorem demonstrates the utterly inevitable and unavoidable formation of spacetime singularities under physically reasonable assumptions, and it remains one of the main results in our understanding of black holes. It is standard lore that quantum gravitational effects will always tame these singularities in black hole interiors. However, the Penrose's theorem provides no clue as to the possible (non-singular) geometries that may be realized in theories beyond general relativity as the result of singularity regularization. In this paper we analyze this problem in spherically symmetric situations, being completely general otherwise, in particular regarding the dynamics of the gravitational and matter fields. Our main result is that, contrary to what one might expect, the set of regular geometries that arises is remarkably limited. We rederive geometries that have been analyzed before, but also uncover some new possibilities. Moreover, the complete catalogue of possibilities that we obtain allows us to draw the novel conclusion that there is a clear tradeoff between internal and external consistency: One has to choose between models that display internal inconsistencies, or models that include significant deviations with respect to general relativity, which should therefore be amenable to observational tests via multi-messenger astrophysics.