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

Jie Jiang,Ming Zhang

doi:10.1140/epjc/s10052-020-8413-9

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.

Highlights

Newman (KN) black hole can be destroyed by absorbing a test particle [2]
Because we assume that the spacetime settles down to a static state in the asymptotic future, checking the validity of the weak cosmic censorship conjecture (WCCC) is equivalent to see whether the line element at sufficient late times describes a black hole, i.e., there exists at least one root of the blacking factor f (r, λ)
There are a lot of investigations to test the weak cosmic censorship in various spacetimes background based on the new version of the gedanken experiments

Summary

Introduction

Newman (KN) black hole can be destroyed by absorbing a test particle [2]. As a result, they found that the extremal KN black holes cannot be overspun or overcharged in this process under the first-order approximation. Sorce and Wald pointed out that if we consider the second-order correction, the spacetime cannot be treated as a background and we need to consider the full dynamical process of the spacetime and perturbation matter They proposed a new version of the gedanken experiments to overspin or overcharge the nearly KN black holes [25]. Based on the Noether charge method [26], they considered the second-order corrections of the energy, angular momenta, and charge of the RN black hole, and derived a perturbation inequality at second-order approximation They concluded that these nearly extremal KN black holes cannot be destroyed after the second-order inequality are taken into consideration.

Linearly charged dilaton-Lifshitz black holes with the spherical perturbation

Perturbation inequalities

Gedanken experiments to destroy the nearly extremal black holes

Conclusion