Stability properties of Regular Black Holes

TL;DR

This paper reviews the stability of regular black holes, focusing on the mass-inflation effect at inner horizons and recent developments that mitigate this instability, including effects of Hawking radiation.

Contribution

It provides a comparative analysis of mass-inflation in regular versus standard black holes and discusses recent advances in understanding their late-time stability.

Findings

Mass-inflation can cause instability at inner horizons of regular black holes.

Hawking radiation influences late-time stability, reducing exponential growth.

Regular black holes exhibit different stability properties compared to classical solutions.

Abstract

Black holes encountered in general relativity are characterized by spacetime singularities hidden within an event horizon. These singularities provide a key motivation to go beyond general relativity and look for regular black holes where the spacetime curvature remains bounded everywhere. A prominent mechanism achieving this replaces the singularity by a regular patch of de Sitter space. The resulting regular geometries exhibit two horizons: the outer event horizon is supplemented by an inner Cauchy horizon. The latter could render the geometry unstable against perturbations through the so-called mass-inflation effect, i.e., an exponential growth of the mass function. This chapter reviews the mass-inflation effect for spherically symmetric black hole spacetimes contrasting the dynamics of the mass function for Reissner-Nordst\"om and regular black holes. We also cover recent developments related to the late-time attractors induced by Hawking radiation which exorcise the exponential growth of the spacetime curvature encountered in the standard mass-inflation scenario. In order to make the exposition self-contained, we also briefly discuss basic properties of regular black holes including their thermodynamics.