Weak Cosmic Censorship Conjecture in Gedanken Experiments at All Orders

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.