New Gedanken experiment on RN-AdS black holes surrounded by quintessence

In this paper, we use the new version of Gedanken experiment to investigate the weak cosmic censorship conjecture(WCCC) for RN-AdS black holes surrounded by quintessence. The process of matter fields falling into the black hole can be regarded as a dynamic process. 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 the stability condition and the null energy condition, the first-order and second-order perturbation inequalities are derived. As a result, we show that the WCCC for RN-AdS black holes surrounded by quintessence cannot be violated under the second-order approximation of matter fields perturbation.