New Gedanken experiment on Reissner-Nordstr\"om AdS Black Holes surrounded by quintessence

TL;DR

This paper uses a new thought experiment to test the weak cosmic censorship conjecture for Reissner-Nordström AdS black holes with quintessence, confirming the conjecture's validity under specific perturbations.

Contribution

It introduces a novel Gedanken experiment approach and applies Iyer-Wald formalism to analyze stability and censorship in black holes surrounded by quintessence.

Findings

Weak cosmic censorship remains valid under second-order perturbations.

Derived first and second-order perturbation inequalities.

Established stability conditions for black holes with quintessence.

Abstract

In this paper, we apply the new Gedanken experiment to investigate the weak cosmic censorship conjecture for Reissner-Nordstr\"om AdS black holes surrounded by quintessence. Since the perturbation of matter fields doesn't affect the spacetime geometry, we propose the stability condition and assume the process of matter fields falling into the black hole satisfies the null energy condition. Based on Iyer-Wald formalism we can derive the first order and second-order variational identities. From the two identities and the above two conditions lead to the first-order and second-order perturbation inequalities, and under the second-order approximation of matter fields perturbation, we find that the weak cosmic censorship conjecture is still satisfied.