Analyzing WGC and WCCC through charged scalar fields fluxes with charged AdS black holes surrounded by perfect fluid dark matter in the CFT thermodynamics

In this paper, we conduct a comprehensive investigation into the weak cosmic censorship conjecture (WCCC) for Reissner-Nordström (R-N) AdS black holes that are influenced by Perfect Fluid Dark Matter (PFDM). Our study is framed within the context of Conformal Field Theory (CFT) thermodynamics. We delve into the principles of energy flux and mass-energy equivalence to explore the interplay between the weak gravity conjecture (WGC) and the WCCC. Our analysis begins by examining the interaction between incoming and outgoing energy fluxes, which induces changes in the black hole's properties. By applying the first law of thermodynamics, we assess the validity of the second law in these dynamic scenarios. We also consider equilibrium conditions that involve both absorption and superradiance processes. Utilizing the framework of black hole thermodynamics within CFT, we demonstrate that the WCCC is upheld if the black hole is in or near an extremal state, particularly when it is subjected to radiation and particle absorption. This finding is significant as it reinforces the robustness of the WCCC under these specific conditions. Furthermore, we uncover additional insights by employing mass-energy equivalence principles and conducting second-order approximations near the extremality state. Specifically, we find that when a black hole radiates and its central charge surpasses the scaled electric charge, the emitted superradiant particles adhere to the WGC. This adherence results in the black hole moving away from its extremal state, thereby maintaining the WCCC.