Addendum to "Strong cosmic censorship: The nonlinear story"

TL;DR

This paper examines the nonlinear stability of the Cauchy horizon in charged black hole spacetimes with a cosmological constant, highlighting the limitations of current numerical methods in assessing Strong Cosmic Censorship violations.

Contribution

It provides new numerical results on charged scalar fields, corrects previous neutral case claims, and discusses the challenges in using existing codes to test SCC near extremal conditions.

Findings

Spectral gap analysis informs linear stability of Cauchy horizons.

Nonlinear effects complicate the assessment of SCC violations.

Current numerical codes are inadequate for conclusive results near extremality.

Abstract

We clarify a number of issues that arise when extending the analysis of Strong Cosmic Censorship (SCC) to perturbations of highly charged Reissner-Nordstr\"{o}m de Sitter (RNdS) spacetimes. The linear stability of the Cauchy horizon can be determined from the spectral gap of quasinormal modes, thus giving a clear idea of the ranges of parameters that are likely to lead to SCC violations for infinitesimally small perturbations. However, the situation becomes much more subtle once nonlinear backreaction is taken into account. These subtleties have created a considerable amount of confusion in the literature regarding the conclusions one is able to derive about SCC from the available numerical simulations. Here we present new numerical results concerning charged self-gravitating scalar fields in spherical symmetry, correct some previous claims concerning the neutral case, and argue that the existing numerical codes are insufficient to draw conclusions about the potential failure of SCC for near extremal RNdS black hole spacetimes.