Abstract
Viewing the negative cosmological constant as a dynamical quantity derived from the matter field, we study the weak cosmic censorship conjecture for the higher-dimensional asymptotically AdS Reissner–Nordström black hole. To this end, using the stability assumption of the matter field perturbation and the null energy condition of the matter field, we first derive the first-order and second-order perturbation inequalities containing the variable cosmological constant and its conjugate quantity for the black hole. We prove that the higher-dimensional RN-AdS black hole cannot be destroyed under a second-order approximation of the matter field perturbation process.
Highlights
The weak cosmic censorship conjecture means that the singularity behind the horizon of the black hole formed by gravitational collapse cannot be exposed by any physical process
It was shown in [1] that the cosmic censorship inequality cannot be violated by adding particle matter with energy E, charge q and angular momentum l, even for extreme black holes
In this article, assuming that the stress–energy tensors of the non-electromagnetic matters do not violate the null energy condition, and the nearly extreme higher-dimensional RNAdS black hole comes to be linearly stable at late times under the perturbation of the matter, we derived the first-order perturbation and the second-order perturbation inequalities
Summary
The weak cosmic censorship conjecture means that the singularity behind the horizon of the black hole formed by gravitational collapse cannot be exposed by any physical process. It was shown in [1] that the cosmic censorship inequality cannot be violated by adding particle matter with energy E, charge q and angular momentum l, even for extreme black holes. Assuming that the nearly extreme Kerr–Newman black hole can still be stable against linear perturbations of the matter field and the null energy condition of the nonelectromagnetic contribution to the matter’s stress–energy tensor is not violated, it was explicitly proved that the conjectured inequality (1) cannot be violated for the black hole This new kind of gedanken experiment has been used to test (1) for other black holes; see, e.g., [18–27]. In [30], it was shown that the weak cosmic censorship conjecture cannot be violated for the nearly extreme higherdimensional RN black hole with the new gedanken experiment.
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