Strong Cosmic Censorship in Kerr-Newman-de Sitter

Abstract: Christodoulou's formulation of Strong Cosmic Censorship (SCC) holds true for Kerr-de Sitter black holes. On the other hand, Reissner-Nordstr\"om-de Sitter black holes violate SCC. We do a detailed scan of the parameter space of Kerr-Newman-de Sitter black holes between these two limiting families, to identify the boundary that marks the transition between solutions that respect and violate SCC. We focus our attention on linear scalar field perturbations. SCC is violated inside a (roughly) `spherical' shell of the parameter space of Kerr-Newman-de Sitter, centred at the corner that describes arbitrarily small extremal Reissner-Nordstr\"om-de Sitter solutions. Outside of this region, including the Kerr-de Sitter limit, we identify perturbation modes that decay slow enough to enforce SCC. Additionally, we do a necessary study of the quasinormal mode spectra of Kerr-Newman-de Sitter in some detail. As established in the literature, in the Kerr-de Sitter and Reissner-Nordstr\"om-de Sitter limits, we find three families of modes: de Sitter, photon sphere and near-horizon modes. These interact non-trivially away from the Reissner-Nordstr\"om-de Sitter limit and display eigenvalue repulsions like in Kerr-Newman black holes.