Inner horizon instability and the unstable cores of regular black holes

TL;DR

This paper investigates the stability of the inner horizons of regular black holes, showing that they are prone to exponential growth of mass due to perturbations, implying that stable nonsingular black holes may not be the final quantum gravity endpoint.

Contribution

The study extends the geometrical framework to regular black holes, demonstrating that their inner horizons are inherently unstable under linear perturbations, challenging the notion of stable nonsingular black hole cores.

Findings

Inner horizons exhibit exponential mass growth due to perturbations.

Stable nonsingular black holes are unlikely as the final quantum gravity state.

Nonperturbative effects are necessary for a consistent quantum gravitational endpoint.

Abstract

Regular black holes with nonsingular cores have been considered in several approaches to quantum gravity, and as agnostic frameworks to address the singularity problem and Hawking's information paradox. While in a recent work we argued that the inner core is destabilized by linear perturbations, opposite claims were raised that regular black holes have in fact stable cores. To reconcile these arguments, we discuss a generalization of the geometrical framework, originally applied to Reissner--Nordtsr\"om black holes by Ori, and show that regular black holes have an exponentially growing Misner--Sharp mass at the inner horizon. This result can be taken as an indication that stable nonsingular black hole spacetimes are not the definitive endpoint of a quantum gravity regularization mechanism, and that nonperturbative backreaction effects must be taken into account in order to provide a consistent description of the quantum-gravitational endpoint of gravitational stellar collapse.