New version of the gedanken experiments to test the weak cosmic censorship in charged dilaton-Lifshitz black holes

TL;DR

This paper uses a new gedanken experiment approach to test the weak cosmic censorship in charged dilaton-Lifshitz black holes, finding that such black holes cannot be destroyed under second-order perturbations, supporting the conjecture's generality.

Contribution

It applies a novel version of the gedanken experiment to charged dilaton-Lifshitz black holes, deriving perturbation inequalities and demonstrating their stability against destruction.

Findings

Nearly extremal black holes cannot be destroyed under second-order perturbations.

Supports the universality of the weak cosmic censorship conjecture in Einstein gravity.

Shows independence from the asymptotic behavior of black holes.

Abstract

In this paper, based on the new version of the gedanken experiments proposed by Sorce and Wald, we examine the weak cosmic censorship in the perturbation process of accreting matter fields for the charged dilaton-Lifshitz black holes. In the investigation, we assume that the black hole is perturbed by some extra matter source satisfied the null energy condition and ultimately settle down to a static charged dilaton-Lifshitz black hole in the asymptotic future. Then, after applying the Noether charge method, we derive the first-order and second-order perturbation inequalities of the perturbation matter fields. As a result, we find that the nearly extremal charged dilaton-Lifshitz black hole cannot be destroyed under the second-order approximation of perturbation. This result implies that the weak cosmic censorship conjecture might be a general feature of the Einstein gravity, and it is independent of the asymptotic behaviors of the black holes.