Violation of Weak Cosmic Censorship in de Sitter Space

Inspired by the recent discovery of a violation of strong cosmic censorship (SCC) for the near-extremal Reissner-Nordstr\"om black holes in de Sitter space (RN-dS), we investigate if the weak cosmic censorship conjecture (WCCC) can also be violated in RN-dS with a fixed cosmological constant. Our method is based on the recent formulation of examining WCCC by requiring the second law to hold, which requires the sum of areas of the event and cosmic horizons cannot decrease during the infall process of Wald's gedanken experiment. We find that the WCCC can be violated for the near-extremal RN-dS in some regimes of second-order perturbation of field configurations. Given the charge parameter of RN-dS, we can find the lowest value of the sub-extremality parameter, beyond which the WCCC holds. Our results imply that violations of SCC and WCCC could be correlated. Because of a lack of an unambiguous relation between the gravitational mass and matter's kinematic mass in asymptotically de Sitter space, we cannot compare the corresponding regimes of parameter space for the violations of SCC and WCCC. We also discuss the subtlety in formulating both the first-law and second-law approaches to examine WCCC.