Weak cosmic censorship conjecture in Einstein-Born-Infeld black holes

TL;DR

This paper investigates the weak cosmic censorship conjecture in Einstein-Born-Infeld black holes, showing that they cannot be overcharged under second-order perturbations, supporting the conjecture's validity in nonlinear electrodynamics contexts.

Contribution

It derives second-order perturbation inequalities for Einstein-Born-Infeld black holes, extending previous results from Einstein-Maxwell gravity and supporting the weak cosmic censorship conjecture.

Findings

Einstein-Born-Infeld black holes cannot be overcharged under second-order perturbations.

The derived inequalities match those in Einstein-Maxwell gravity.

Results suggest the validity of WCCC in string theory-related models.

Abstract

Recently, Sorce and Wald have suggested a new version of the gedanken experiments to overspin or overcharge the Kerr-Newman black holes in Einstein-Maxwell gravity. Following their setup, in this paper, we investigate the weak cosmic censorship conjecture (WCCC) in the static Einstein-Born-Infeld black holes for the Einstein gravity coupled to nonlinear electrodynamics. First of all, we derive the first two order perturbation inequalities of the charged collision matter in the Einstein-Born-Infeld gravity based on the Iyer-Wald formalism as well as the null energy conditions of the matter fields and show that they share the same form as these in Einstein-Maxwell gravity. As a result, we find that the static Einstein-Born-Infeld black holes cannot be overcharged under the second-order approximation after considering these inequalities. Our result at some level hints at the validity of the weak cosmic censorship conjecture for string theory.