Weak Cosmic Censorship Conjecture in Gedanken Experiments at All Orders

TL;DR

This paper systematically analyzes the Weak Cosmic Censorship Conjecture using high-order perturbation Gedankenexperiments on black holes, revealing that the conjecture's validity depends on a specific thermodynamic derivative which is positive for known black holes.

Contribution

It introduces a method to calculate perturbations to any order for a broad class of black holes, linking the WCCC's validity to a thermodynamic quantity.

Findings

WCCC validity hinges on the positivity of a specific thermodynamic derivative.

The derivative $W$ is positive for all well-known black holes.

The approach applies to extremal and near-extremal black holes.

Abstract

We present a systematic analysis of the Weak Cosmic Censorship Conjecture (WCCC) through Gedankenexperiments involving black hole perturbations induced by test particles. Our approach allows for the calculation of perturbations to any order for a general class of black holes that admit the zero-temperature extremal limit. We find that the WCCC for extremal and near-extremal black holes is hinged upon the positive sign of only one quantity, namely $W=\left( \frac{\partial S}{\partial T} \right)_{Q_\alpha ; T=0}$, which is indeed positive for all the well-known black holes.