Examining the weak cosmic censorship conjecture of RN-AdS black holes via the new version of the gedanken experiment

Based on the new version of the gedanken experiment proposed by Sorce and Wald, we investigate the weak cosmic censorship conjecture (WCCC) for Reissner-Nordstrom-AdS (RN-AdS) black holes under the second-order approximation of the perturbation that comes from the matter fields. First of all, we propose that the cosmological constant is a portion of the matter fields. It means that the cosmological constant can be seen as a variable, and its value will vary with the process of the perturbation. Moreover, we assume that the perturbation satisfies the stability condition, which states that after the perturbation, the spacetime geometry also belongs to the class of RN-AdS solutions. Based on the stability condition and the null energy condition, while using the method of the off-shell variation, the first two order perturbation inequalities are derived. In the two inequalities, the term which contains the thermodynamic pressure and volume is involved firstly. Furthermore, based on the first-order optimal option and the second-order inequality, the WCCC for nearly extremal RN-AdS black holes is examined. It is shown that considering the cosmological constant varying with the perturbation, the WCCC for RN-AdS black holes cannot be violated under the second-order approximation of the matter fields perturbation.