Mass inflation without Cauchy horizons

TL;DR

This paper demonstrates that mass inflation, characterized by exponential energy buildup, occurs in dynamical black hole geometries with inner trapping horizons even without Cauchy horizons, broadening the understanding of black hole instability.

Contribution

It introduces a generalized concept of mass inflation applicable to dynamical horizons without Cauchy horizons, extending previous results and implications for black hole evolution.

Findings

Mass inflation occurs without Cauchy horizons in dynamical geometries.

Inner trapping horizons can exhibit significant energy buildup.

Results recover known behaviors when inner horizons approach Cauchy horizons.

Abstract

Mass inflation is a well established instability, conventionally associated to Cauchy horizons (which are also inner trapping horizons) of stationary geometries, leading to a divergent exponential buildup of energy. We show here that finite (but often large) exponential buildups of energy are generically present for dynamical geometries endowed with slowly-evolving inner trapping horizons, even in the absence of Cauchy horizons. This provides a more general definition of mass inflation based on quasi-local concepts. We also show that various known results in the literature are recovered in the limit in which the inner trapping horizon asymptotically approaches a Cauchy horizon. Our results imply that black hole geometries with non-extremal inner horizons, including the Kerr geometry in general relativity, and non-extremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived endpoint of gravitational collapse.