A note on the stability of the Cauchy horizon in regular black holes without mass inflation

TL;DR

This paper investigates the stability of the Cauchy horizon in a specific regular black hole model, finding classical stability but quantum instability, which has implications for black hole physics.

Contribution

It introduces and analyzes a regular black hole with zero surface gravity at the Cauchy horizon, highlighting its classical stability and quantum instability.

Findings

Classical perturbations do not cause mass inflation.

Quantum fluctuations induce instability at the Cauchy horizon.

The model differs from typical regular black holes with nonzero surface gravity.

Abstract

Unlike generic models of regular black holes (BHs) with nonzero surface gravity on both Cauchy and event horizons, an inner-degenerate counterpart with zero Cauchy horizon surface gravity was recently proposed. For this regular BH solution with spherical symmetry, we examine the stability of the Cauchy horizon from both classic and quantum mechanics viewpoints. We find that the classical perturbations do not lead to mass inflation at the Cauchy horizon, indicating classically stability, while quantum fluctuations cause it to be unstable quantum mechanically.