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