Weak Cosmic Censorship Conjecture Cannot be Violated in Gedanken Experiments

TL;DR

This paper systematically investigates the Weak Cosmic Censorship Conjecture (WCCC) using thought experiments with black hole perturbations, concluding that WCCC cannot be violated under various conditions and black hole types.

Contribution

It provides a comprehensive analysis of WCCC violation scenarios, resolves previous contradictions, and demonstrates WCCC's robustness across different black hole configurations.

Findings

WCCC depends on the sign of parameter W, with W>0 preserving it.

WCCC is upheld for spherically symmetric, static, and asymptotically-(A)dS black holes.

The no-hair theorem protects WCCC in general cases.

Abstract

We innovate a systematic investigation of the Weak Cosmic Censorship Conjecture (WCCC) using gedanken experiments involving black hole perturbations by test particles. We classify various WCCC violation scenarios proposed in recent decades, including Hubeny, mixed, and the latest Sorce-Wald (SW). We provide general formulae in each case, and resolve contradictions in numerous studies. Following SW type, our analysis reveals that WCCC depends on the sign choice of the parameter $W\equiv \big(\frac{\partial S}{\partial T}\big)_{Q_i; T=0}$ of the extremal black holes. $W > 0$ preserves WCCC and $W < 0$ would indicate potential violation. We show explicitly that $W>0$ for spherically-symmetric and static black holes, and for general case, we argue that it is protected by the black hole no-hair theorem. We also consider asymptotically-(A)dS black holes and argue that there can be no violation either.