Strong cosmic censorship for charged de Sitter black holes with a charged scalar field

Abstract

It has been shown recently that the strong cosmic censorship conjecture is violated by near-extremal Reissner-Nordstr\"om-de Sitter black holes. We investigate whether the introduction of a charged scalar field can rescue strong cosmic censorship. We find that such a field improves the situation but there is always a neighbourhood of extremality in which strong cosmic censorship is violated by perturbations arising from smooth initial data.