New version of the gedanken experiments to test the weak cosmic censorship in charged dilaton-Lifshitz black holes
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Regular Article - Theoretical Physics
New version of the gedanken experiments to test the weak cosmic censorship in charged dilaton-Lifshitz black holes Jie Jiang1,a , Ming Zhang2,b 1 2
Department of Physics, Beijing Normal University, Beijing 100875, China Department of Physics, Jiangxi Normal University, Nanchang 330022, China
Received: 28 February 2020 / Accepted: 27 August 2020 © The Author(s) 2020
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.
1 Introduction The general relativity predicts the existence of the black hole. There is a central singularity for most of the black holes. However, the singularity will make the spacetime ill-defined and destroy the law of causality. Therefore, Penrose proposed the weak cosmic censorship conjecture (WCCC) to ensure the predictability in the physical spacetime region [1]. This conjecture states that all singularities caused by the gravitational collapsing body must be hidden inside an event horizon such that it does not affect the causality outside the black. hole. It also means that the black holes cannot be destroyed by any physical process once it is formed if there is a singularity inside the event horizon. To test this conjecture, Wald proposed a gedanken experiment to check whether the Kerra e-mail:
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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. However, there are two drawbacks to this discussion, i.e., the initial black hole is extreme and it is only at the level of the first-order perturbation. For this story to be truly consistent, Hubeny extended the discussion to the second-order case in the nearly extremal KN black holes and showed that the nearly black hole can be destroyed in this case [3] when the second-order effects are neglected. Their result attracted lots of researchers to extend it into various theories [4–24]. Recently, Sorce and Wald pointed out that if we consider the
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