A note on strong cosmic censorship and its violation in Reissner–Nordström de Sitter black hole space-times

Abstract

Penrose’s strong cosmic censorship (SCC) conjecture safeguards determinism in general relativity (GR). Within the initial value approach to GR, proof of SCC preservation is predicated on the unique evolution of the metric. For the Kerr–Newman family of black hole solutions, this requires the inextendibility of the metric past the Cauchy horizon, due to the development of a ‘blue-shift’ instability. Attempts to provide a rigorous mathematical proof of SCC has led to the formulation of several SCC 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 SCC preservation, with a focus on the Reissner–Nordström de Sitter (RNdS) 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 SCC conjecture within RNdS black holes.