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

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.