Static charged dilaton black hole cannot be overcharged by gedanken experiments

TL;DR

This paper demonstrates that static charged dilaton black holes cannot be overcharged through gedanken experiments once second-order perturbation effects are considered, thus supporting the weak cosmic censorship conjecture.

Contribution

It derives first- and second-order perturbation inequalities in Einstein-Maxwell-dilaton gravity, showing the conjecture's protection against overcharging in this context.

Findings

Weak cosmic censorship is upheld with second-order effects.

Overcharging is prevented when considering second-order perturbations.

The conjecture is violated only without second-order considerations.

Abstract

We consider the new version of the gedanken experiments proposed recently by Sorce and Wald to overcharge a static charged dilaton black hole. First of all, we derive the first-order and second-order perturbation inequalities in the Einstein-Maxwell-dilaton gravitational theory based on the Iyer-Wald formalism. As a result, we find that the weak cosmic censorship conjecture associated with this black hole can be protected after taking into account the second-order perturbation inequality, although violated by the scene without considering this inequality. Therefore, there is no violation of the weak cosmic censorship conjecture around the charged static dilaton black holes in Einstein-Maxwell-dilaton gravity