Mass inflation inside black holes revisited

TL;DR

This paper revisits the mass inflation phenomenon inside black holes, showing that considering the local inner apparent horizon instead of the global Cauchy horizon alters the understanding of back-reaction effects, reducing singularities.

Contribution

It derives a new spherically symmetric back-reaction solution near the inner apparent horizon, accounting for its separation from the Cauchy horizon, and shows this removes the infinite blue-shift singularity.

Findings

Back-reaction perturbations are largest at the inner apparent horizon but remain small.

The new solution removes the infinite blue-shift singularity at the horizons.

Considering the local horizon changes the mass inflation analysis.

Abstract

The mass inflation phenomenon implies that black hole interiors are unstable due to a back-reaction divergence of the perturbed black hole mass function at the Cauchy horizon. Weak point in the standard mass inflation calculations is in a fallacious using of the global Cauchy horizon as a place for the maximal growth of the back-reaction perturbations instead of the local inner apparent horizon. It is derived the new spherically symmetric back-reaction solution for two counter-streaming light-like fluxes near the inner apparent horizon of the charged black hole by taking into account its separation from the Cauchy horizon. In this solution the back-reaction perturbations of the background metric are truly the largest at the inner apparent horizon, but, nevertheless, remain small. The back reaction, additionally, removes the infinite blue-shift singularity at the inner apparent horizon and at the Cauchy horizon.