Cauchy Horizon (In)Stability of Regular Black Holes

TL;DR

This paper investigates the stability of Cauchy horizons in regular black holes, revealing that certain models exhibit power-law or logarithmic mass growth, which affects their susceptibility to the mass-inflation instability.

Contribution

It extends previous analyses by identifying the basin-of-attraction for power-law mass growth and applying the analysis to new black hole models, including those from quantum gravity.

Findings

Power-law mass growth is generic in certain regular black holes.

The Dymnikova and Bardeen black holes exhibit similar stability features.

A non-singular collapse model shows only logarithmic mass growth at the Cauchy horizon.

Abstract

A common feature of regular black hole spacetimes is the presence of an inner Cauchy horizon. The analogy to the Reissner-Nordstr\"om solution then suggests that these geometries suffer from a mass-inflation effect, rendering the Cauchy horizon unstable. Recently, it was shown that this analogy fails for certain classes of regular black holes, including the Hayward solution, where the late-time behavior of the mass function no longer grows exponentially but follows a power law. In this work, we extend these results in a two-fold way. First, we determine the basin-of-attraction for the power-law attractor, showing that the tamed growth of the mass function is generic. Second, we extend the systematic analysis to the Bardeen geometry, the Dymnikova black hole, and a spacetime arising from a non-singular collapse model newly proposed in the context of asymptotically safe quantum gravity. Remarkably, in the latter solution, the Misner-Sharp mass at the Cauchy horizon remains of the same order of magnitude of the mass of the black hole, since its growth is just logarithmic.