Classical stability and quantum instability of black-hole Cauchy horizons

TL;DR

This paper investigates the stability of black hole Cauchy horizons, showing classical stability in certain cases but arguing that quantum effects inevitably cause instability, impacting predictability in black hole physics.

Contribution

It demonstrates classical stability conditions and proves quantum instability of Cauchy horizons in Reissner-Nordström-de Sitter black holes.

Findings

Classical stability exists for specific parameter ranges.

Quantum effects induce instability regardless of classical stability.

Implications for predictability in black hole evolution.

Abstract

For a certain region of the parameter space $\{M,e,\Lambda\}$, the Cauchy horizon of a (charged) black hole residing in de Sitter space is classically stable to gravitational perturbations. This implies that, when left to its own devices, classical theory is unable to retain full predictive power: the evolution of physical fields beyond the Cauchy horizon is not uniquely determined by the initial conditions. In this paper we argue that the Cauchy horizon of a Reissner-Nordstr\"om-de Sitter black hole must always be unstable quantum mechanically.