It is proved that dynamically formed Reissner-Nordstr?m-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 thatchargedmassive scalar fields in the charged RNdS black-hole spacetime are characterized, in the large-coupling regime, by quasinormal resonant frequencies with?ωmin<12κ+, whereκ+is the surface gravity of the black-hole event horizon. This result implies that the corresponding relaxation rateψ～e??ωmintof 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 ofchargedmatter fields in dynamically formedchargedspacetimes, non-asymptotically flat RNdS black holes are globally hyperbolic and therefore respect the fundamental strong cosmic censorship conjecture.
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