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

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.