Holographic CFT Thermodynamics as a Bridge Between the Weak Gravity and Weak Cosmic Censorship Conjectures for EMPYM--AdS Black Holes

Abstract

The weak cosmic censorship conjecture (\WCCC) and the weak gravity conjecture (\WGC) sit at the heart of how singularities and charged matter are constrained in any consistent theory of quantum gravity. We study both conjectures for Einstein--Maxwell--power--Yang--Mills--AdS (\EMPYM) black holes, a family in which a non-Abelian power-law Yang--Mills field, a Maxwell field, and a negative cosmological constant act together. Working in holographic conformal field theory (CFT) thermodynamics, we treat the central charge $C$ and the CFT volume $\Vol$ as independent variables and obtain an extended first law that carries variations of the Yang--Mills charge and of the nonlinearity exponent $\gamma$. A closed Euler relation follows, and we check it together with the full set of equations of state to machine precision. The perturbation is a charged massive scalar minimally coupled to the Maxwell sector. Its horizon energy and charge fluxes fix the superradiance threshold $\omega<\tilde{q}_s\tilde{\phi}_h$, and the mass--energy relation $\mu_s=\omega$ turns this into the bound $\tilde{q}_s/\mu_s>r_{\min}/\tilde{Q}$. Expanding the metric function $f(r)$ about its minimum for extremal and near-extremal configurations, we find that absorption keeps $f_{\min}$ non-positive, so the horizon survives. The Yang--Mills sector lowers the effective charge-to-mass threshold below the Reissner--Nordstr\"om value of unity, while a local stability analysis locates a Davies point in the heat capacity. Across the parameter range examined the \EMPYM\ family respects cosmic censorship under scalar perturbations, with the \WGC\ fixing only the direction of evolution toward or away from extremality.