A note on Strong Cosmic Censorship and its violation in Reissner-Nordstr\'om de Sitter black hole space-times

Penrose's Strong Cosmic Censorship conjecture safeguards determinism in General Relativity. Within the initial value approach to General Relativity, proof of Strong Cosmic Censorship preservation is predicated on the unique evolution of the metric. For the Kerr-Newman family of black hole solutions, this requires the inextendability of the metric past the Cauchy horizon, due to the development of a "blue-shift" instability. Attempts to provide a rigorous mathematical proof of Strong Cosmic Censorship has led to the formulation of several Strong Cosmic Censorship conjectures of varying strengths, which seem to be discussed rarely outside of the mathematical relativity literature. In this note, we review some of the arguments for and against Strong Cosmic Censorship preservation, with a focus on the Reissner-Nordstr\"om de Sitter context, where the positive cosmological constant invites a "red-shift" effect that competes against the "blue-shift". We study the consequent role of quasinormal mode behaviour and illustrate the parameter space for which we consistently observe violations of the Strong Cosmic Censorship conjecture within Reissner-Nordstr\"om de Sitter black holes.
Comment: 30 pages, 8 figures. This manuscript has some overlap with arXiv:2310.07311 and an ICHEP2024 proceeding available at https://doi.org/10.22323/1.476.0782