Gravitational Collapse and Cosmic Censorship

TL;DR

The paper surveys the status of the weak cosmic censorship conjecture, arguing that although a general proof is elusive, substantial evidence from black hole stability and the nonexistence of robust counterexamples supports its validity. It carefully formulates the conjecture for asymptotically flat spacetimes, discusses genericity and suitable matter, and reviews key results such as linear stability of Schwarzschild and Kerr, isoperimetric-type bounds, and hoop conjecture discussions. A crucial focus is on the spherically symmetric Einstein–Klein–Gordon system, where Christodoulou demonstrates naked singularities can arise for special data while also establishing a non-genericity theorem, and Choptuik reveals universal critical phenomena near collapse. Together, these insights suggest weak cosmic censorship remains plausible and physically relevant, though a comprehensive, general proof remains outstanding.

Abstract

We review the status of the weak cosmic censorship conjecture, which asserts, in essence, that all singularities of gravitational collapse are hidden within black holes. Although little progress has been made toward a general proof (or disproof) of this conjecture, there has been some notable recent progress in the study of some examples and special cases related to the conjecture. These results support the view that naked singularities cannot arise generically.