The topological RN-AdS black holes cannot be overcharged by the new version of gedanken experiment

TL;DR

This paper demonstrates that topological RN-AdS black holes in higher dimensions cannot be overcharged, supporting the weak cosmic censorship conjecture using a refined gedanken experiment that accounts for second-order effects.

Contribution

It applies a new second-order perturbation method to test the WCCC for topological RN-AdS black holes, confirming their stability against overcharging.

Findings

Black holes cannot be overcharged under second-order perturbations.

The WCCC holds for topological RN-AdS black holes in higher dimensions.

Violation of Hubeny type does not occur in these scenarios.

Abstract

In this paper, we test the weak cosmic censorship conjecture (WCCC) for n >= 4 dimensional nearly extremal RN-AdS black holes with non-trivial topologies, namely plane and hyperbola, using the new version of gedanken experiment proposed by Sorce and Wald. Provided that the non-electromagnetic part of the stress tensor of matter fields satisfies the null energy condition and the linear stability condition holds, we find that the black holes cannot be overcharged under the second-order perturbation approximation, which includes the self-force and finite-size effects. As a result, we conclude that the violation of Hubeny type never occurs and the WCCC holds for the topological RN-AdS black hole.