# Opening the Pandora's box at the core of black holes

## TL;DR

This paper classifies all possible spherically symmetric spacetimes resulting from singularity regularization, revealing limited possibilities and a strong link between deviations from general relativity and internal consistency, impacting black hole physics and quantum gravity tests.

## Contribution

It provides a comprehensive geometric classification of regularized black hole spacetimes applicable to all modified gravity and quantum gravity effective theories.

## Key findings

- Limited classes of geometries (no more than a few)
- Strong correlation between deviations from GR and internal consistency
- Implications for black hole understanding and quantum gravity tests

## Abstract

Unless the reality of spacetime singularities is assumed, astrophysical black holes cannot be identical to their mathematical counterparts obtained as solutions of the Einstein field equations. Mechanisms for singularity regularization would spark deviations with respect to the predictions of general relativity, although these deviations are generally presumed to be negligible for all practical purposes. Nonetheless, the strength and nature of these deviations remain open questions, given the present uncertainties about the dynamics of quantum gravity. We present here a geometric classification of all spherically symmetric spacetimes that could result from singularity regularization, using a kinematic construction that is both exhaustive and oblivious to the dynamics of the fields involved. Due to the minimal geometric assumptions behind it, this classification encompasses virtually all modified gravity theories, and any theory of quantum gravity in which an effective description in terms of an effective metric is available. The first noteworthy conclusion of our analysis is that the number of independent classes of geometries that can be constructed is remarkably limited, with no more than a handful of qualitatively different possibilities. But our most surprising result is that this catalogue of possibilities clearly demonstrates that the degree of internal consistency and the strength of deviations with respect to general relativity are strongly, and positively, correlated. Hence, either quantum fluctuations of spacetime come to the rescue and solve these internal consistency issues, or singularity regularization will percolate to macroscopic (near-horizon) scales, radically changing our understanding of black holes and opening new opportunities to test quantum gravity.