Violation of weak cosmic censorship by the Oppenheimer-Snyder collapse

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.