Strong cosmic censorship: taking the rough with the smooth

TL;DR

This paper demonstrates that for near-extremal Reissner-Nordström-de Sitter black holes, smooth initial perturbations can be extended beyond the Cauchy horizon, challenging traditional views on strong cosmic censorship and emphasizing the importance of rough initial data.

Contribution

It shows that coupled gravitational and electromagnetic perturbations can violate strong cosmic censorship for smooth initial data, resolving a contradiction by highlighting the role of non-smooth initial data.

Findings

Perturbations extend smoothly through the Cauchy horizon in near-extremal black holes.

Smooth initial data can lead to violations of strong cosmic censorship.

The old argument for censorship applies only to non-smooth initial data.

Abstract

It has been argued that the strong cosmic censorship conjecture is violated by Reissner-Nordstr\"om-de Sitter black holes: for near-extremal black holes, generic scalar field perturbations arising from smooth initial data have finite energy at the Cauchy horizon even though they are not continuously differentiable there. In this paper, we consider the analogous problem for coupled gravitational and electromagnetic perturbations. We find that such perturbations exhibit a much worse violation of strong cosmic censorship: for a sufficiently large near-extremal black hole, perturbations arising from smooth initial data can be extended through the Cauchy horizon in an arbitrarily smooth way. This is in apparent contradiction with an old argument in favour of strong cosmic censorship. We resolve this contradiction by showing that this old argument is valid only for initial data that is not smooth. This is in agreement with the recent proposal that, to recover strong cosmic censorship, one must allow rough initial data.