Weak Cosmic Censorship Conjecture Cannot be Violated in Gedanken Experiments

TL;DR

This work addresses whether the Weak Cosmic Censorship Conjecture (WCCC) can be violated when a black hole is perturbed by test particles. It introduces a unified, order-aware framework that classifies prior attempts into Hubeny's type, mixed type, and Sorce-Wald (SW) type, and defines the horizon-stability parameter $W=\lim_{T\to0}(\partial S/\partial T)_{Q_i}$. By deriving general formulae for each type and analyzing near-extremal and extremal limits, the authors show that $W>0$ for extremal black holes and, in general, for spherically symmetric/static cases, which protects WCCC; extremal cases remain robust even if $W<0$ in some scenarios. They also extend the reasoning to asymptotically (A)dS spacetimes, arguing no violations arise, and discuss implications for no-hair, higher-order gravities, and potential quantum/back-reaction corrections. Overall, the paper provides a concise, broadly applicable framework to resolve historical contradictions and guides future investigations of WCCC in diverse black hole spacetimes.

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.