Violation of weak cosmic censorship by the Oppenheimer-Snyder collapse

TL;DR

This paper explores whether the weak cosmic censorship conjecture can be violated through the Oppenheimer-Snyder collapse model, analyzing various theoretical scenarios and their physical viability, and highlighting the challenges in constructing such violations.

Contribution

It systematically examines models and conditions under which weak cosmic censorship might be violated, emphasizing the limitations and potential pathways involving modified gravity or thin-shell constructions.

Findings

No physically viable model found that violates weak cosmic censorship.

Violations may be possible in modified gravity models without shells.

Thin-shell approaches approach naked singularities without energy condition violations.

Abstract

We consider the possibility that the weak cosmic censorship conjecture can be violated using the Oppenheimer-Snyder collapse model with a perfect fluid star interior. Metric models with a naked singularity can be used, and the Oppenheimer-Snyder collapse might be possible; the null energy condition is also satisfied in these models. However, this is just a toy model because no known model as a solution to the Einstein equation. To avoid this problem, we can consider a naked singularity solution as a proper solution of the Einstein equation, but in this case, we need to introduce a thin-shell on top of the perfect fluid star. In this case, gravitational collapse is allowed, but the null energy condition should be violated at the thin-shell. In conclusion, we could not find a physically viable model that violates weak cosmic censorship, but it opens a window to study the properties of cosmic censorship constructively. The violation of weak cosmic censorship might be possible if a modified gravity model provides a solution that allows the Oppenheimer-Snyder collapse without a shell. Also, regarding the thin-shell case, the shell approaches the naked singularity closer without violating the null energy condition, although it must violate the null energy condition at the singularity eventually; this might be regarded as an effective violation of cosmic censorship in some sense.