Regular black holes without mass inflation instability

TL;DR

This paper introduces a class of regular black holes with a vanishing inner horizon surface gravity, eliminating the mass inflation instability and making them more stable and viable as alternatives to singular black holes.

Contribution

It demonstrates how to construct regular black hole geometries with zero inner horizon surface gravity while maintaining other properties, avoiding mass inflation instability.

Findings

Inner-extremal black holes lack mass inflation instability

Constructed geometries show stability under perturbations

These black holes are better behaved than singular and generic regular black holes

Abstract

Generic models of regular black holes have separate outer and inner horizons, both with nonzero surface gravity. It has been shown that a nonzero inner horizon surface gravity results in exponential instability at the inner horizon controlled by this parameter. This phenomenon takes the name of "mass inflation instability", and its presence has put in question the physical viability of regular black holes as alternatives to their (singular) general relativity counterparts. In this paper, we show that it is possible to make the inner horizon surface gravity vanish, while maintaining the separation between horizons, and a non-zero outer horizon surface gravity. We construct specific geometries satisfying these requirements, and analyze their behavior under different kinds of perturbations, showing that the exponential growth characteristic of mass inflation instability is not present for these geometries. These "inner-extremal" regular black holes are thereby better behaved than singular black holes and generic regular black holes, thus providing a well-motivated alternative of interest for fundamental and phenomenological studies.