Testing the weak cosmic censorship conjecture in the massive gravitational theories

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 process of accreting matter fields for nearly extremal static charged black holes in the massive gravitational theories coupled to a Maxwell field. In the investigation, we assume that the black hole is perturbed by some matter fields satisfied null energy condition and ultimately settles down to a static state in the asymptotic future. Moreover, we also treat the cosmological constant, the graviton mass, and the coupling constants as variables, and they can be affected by the physical process. 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 black hole cannot be destroyed under the second-order approximation of perturbation. This result implies that the weak cosmic censorship conjecture is satisfied in the gravitational theories with massive graviton.