Weak cosmic censorship conjecture in higher-dimensional black holes with nonlinear electrodynamic sources

TL;DR

This paper tests the weak cosmic censorship conjecture in higher-dimensional black holes with nonlinear electrodynamics, showing that such black holes cannot be overcharged, supporting the conjecture's validity in these systems.

Contribution

It extends the Sorce-Wald gedanken experiment framework to higher-dimensional nonlinear electrodynamics black holes, deriving perturbation inequalities and demonstrating their stability against overcharging.

Findings

Higher-dimensional nonlinear electrodynamics black holes cannot be overcharged.

Perturbation inequalities similar to Einstein-Maxwell gravity are derived.

Results support the validity of WCCC in more general systems.

Abstract

The new version of the gedanken experiments proposed by Sorce and Wald are designed to test the validity of the weak cosmic censorship conjecture (WCCC) by overspinning or overcharging the Kerr-Newman black hole in Einstein-Maxwell gravity. Following their setup, in this paper, we investigate the WCCC in the higher-dimensional charged black hole with a nonlinear electrodynamics source. We derive the first and seconder order perturbation inequalities of the charged collision matter based on the Iyer-Wald formalism as well as the null energy conditions, and show that they share the similar form as that in Einstein-Maxwell gravity. As a result, we find that the static higher-dimensional nonlinear electrodynamics (HDNL) black holes cannot be overcharged after considering these two inequalities. Our result might indicate the validity of WCCC for more general HNDL and related systems.