Strong cosmic censorship in charged black-hole spacetimes: As strong as ever

TL;DR

This paper proves that charged black holes in de Sitter space have unstable inner horizons, supporting the strong cosmic censorship conjecture by showing that charge and scalar fields lead to horizon instability.

Contribution

It provides an analytical proof that charged scalar fields cause instability of inner horizons in charged black holes, reaffirming the strong cosmic censorship in these spacetimes.

Findings

Inner Cauchy horizons are unstable due to charged scalar fields.

Quasinormal frequencies have imaginary parts less than half the surface gravity.

Charged matter fields ensure the global hyperbolicity of charged black holes.

Abstract

It is proved that dynamically formed Reissner-Nordstr\"om-de Sitter (RNdS) black holes, which have recently been claimed to provide counter-examples to the Penrose strong cosmic censorship conjecture, are characterized by unstable (singular) inner Cauchy horizons. The proof is based on analytical techniques which explicitly reveal the fact that {\it charged} massive scalar fields in the charged RNdS black-hole spacetime are characterized, in the large-coupling regime, by quasinormal resonant frequencies with $\Im\omega^{\text{min}}<{1\over2}\kappa_+$, where $\kappa_+$ is the surface gravity of the black-hole event horizon. This result implies that the corresponding relaxation rate $\psi\sim e^{-\Im\omega^{\text{min}}t}$ of the collapsed charged fields is slow enough to guarantee, through the mass-inflation mechanism, the instability of the dynamically formed inner Cauchy horizons. Our results reveal the physically important fact that, taking into account the unavoidable presence of {\it charged} matter fields in dynamically formed {\it charged} spacetimes, non-asymptotically flat RNdS black holes are globally hyperbolic and therefore respect the fundamental strong cosmic censorship conjecture.