Cosmic censorship: As strong as ever

Spacetimes which have been considered counterexamples to strong cosmic censorship are revisited. We demonstrate the classical instability of the Cauchy horizon inside charged black holes embedded in de Sitter spacetime for all values of the physical parameters. The relevant modes that maintain the instability, in the regime which was previously considered stable, originate as outgoing modes near the black-hole event horizon. This same mechanism is also relevant for the instability of Cauchy horizons in other proposed counterexamples to strong cosmic censorship.