Strong cosmic censorship conjecture with NUT charge and conformal coupling

TL;DR

This paper investigates how NUT charge and conformal scalar fields influence the violation of the strong cosmic censorship conjecture in charged de Sitter black holes, finding violations under certain conditions but not in rotating black holes with NUT charge.

Contribution

It demonstrates that NUT charge and conformal coupling can lead to violations of the strong cosmic censorship conjecture in specific black hole spacetimes, extending previous understanding.

Findings

Violations occur in charged de Sitter black holes with NUT charge and conformal scalar fields.

Conformal coupling worsens the extendibility of scalar fields across the Cauchy horizon.

Strong cosmic censorship is respected in rotating black holes with NUT charge.

Abstract

Strong cosmic censorship conjecture is central to the deterministic nature of general relativity, since it asserts that given any generic initial data on a spacelike hypersurface, the future can be uniquely predicted. However, recently it has been found that for charged black holes in asymptotically de Sitter spacetimes, the metric and massless scalar fields can be extended beyond the Cauchy horizon. This spells doom on the strong cosmic censorship conjecture, which prohibits precisely this scenario. In this work we try to understand the genericness of the above situation by studying the effect of NUT charge and conformally coupled scalar field on the violation of strong cosmic censorship conjecture for charged asymptotically de Sitter black holes. We have shown that even in the presence of the NUT charge and a conformally coupled scalar field strong cosmic censorship conjecture in indeed violated for such black holes with Cauchy horizon. Moreover, the presence of conformal coupling makes the situation even worse, in the sense that the scalar field is extendible across the Cauchy horizon as a $C^{1}$ function. On the other hand, the strong cosmic censorship conjecture is respected for conformally coupled scalar field in rotating black hole spacetimes with NUT charge. This reinforces the belief that possibly for astrophysical black holes, strong cosmic censorship conjecture is respected, irrespective of the nature of the scalar field.