Regular evaporating black holes with stable cores

TL;DR

This paper investigates how Hawking radiation influences the stability of regular black holes with Cauchy horizons, revealing two late-time behaviors that can weaken or eliminate the mass-inflation instability.

Contribution

First dynamical analysis of mass-inflation effect considering black hole mass-loss due to Hawking radiation, identifying two distinct late-time behaviors.

Findings

Hawking flux determines late-time behavior of black hole interiors.

Regular black holes of Hayward and RG-improved types develop a $v^6$ curvature growth.

Reissner-Nordström and Bardeen black holes maintain finite curvature scalars at late times.

Abstract

A feature shared by many regular black hole spacetimes is the occurrence of a Cauchy horizon. It is then commonly believed that this renders the geometry unstable against perturbations through the mass-inflation effect. In this work, we perform the first dynamical study of this effect taking into account the mass-loss of the black hole due to Hawking radiation. It is shown that the time-dependence of the background leads to two novel types of late-time behavior whose properties are entirely determined by the Hawking flux. The first class of attractor-behavior is operative for regular black holes of the Hayward and renormalization group improved type and characterized by the square of the Weyl curvature growing as $v^6$ at asymptotically late times. This singularity is inaccessible to a radially free-falling observer though. The second class is realized by Reissner-Nordstr{\"o}m black holes and regular black holes of the Bardeen type. In this case the curvature scalars remain finite as $v\rightarrow\infty$. Thus the Hawking flux has a profound effect on the mass-inflation instability, either weakening the effect significantly or even expelling it entirely.