AI 中文总结
研究爱因斯坦 - 麦克斯韦 - 幂 - 杨 - 米尔斯 - 反德西特黑洞的弱宇宙审查和弱引力猜想，通过全息共形场论热力学得出扩展第一定律及欧拉关系，经微扰分析等得出该家族在标量微扰下尊重宇宙审查，明确了演化方向。
AI 中文摘要
弱宇宙审查猜想（\WCCC）和弱引力猜想（\WGC）是量子引力理论中奇点和带电物质如何被约束的核心。我们研究了爱因斯坦 - 麦克斯韦 - 幂 - 杨 - 米尔斯 - 反德西特（\EMPYM）黑洞的这两个猜想，该黑洞家族中一个非阿贝尔幂律杨 - 米尔斯场、一个麦克斯韦场和一个负宇宙学常数共同作用。在全息共形场论（CFT）热力学中，将中心荷\(C\)和CFT体积\(\Vol\)视为独立变量，得到一个扩展的第一定律，它包含杨 - 米尔斯荷和非线性指数\(\gamma\)的变化。由此得出一个封闭的欧拉关系，并以机器精度检查了全套状态方程。微扰是一个与麦克斯韦部分最小耦合的带电大质量标量。其视界能量和电荷通量确定了超辐射阈值\(\omega<\tilde{q}_s\tilde{\phi}_h\)，质量 - 能量关系\(\mu_s=\omega\)将其转化为\(\tilde{q}_s/\mu_s>r_{\min}/\tilde{Q}\)的界限。对极端和近极端构型的度规函数\(f(r)\)在其最小值附近展开，发现吸收使\(f_{\min}\)非正，所以视界得以保留。杨 - 米尔斯部分将有效荷质比阈值降低到低于雷斯纳 - 诺德斯特龙的单位值，而局部稳定性分析在热容量中定位了一个戴维斯点。在所研究的参数范围内，\EMPYM\)家族在标量微扰下尊重宇宙审查，\WGC\)仅确定了朝向或远离极端性的演化方向。
英文摘要
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 $γ$. 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 $ω<\tilde{q}_s\tildeϕ_h$, and the mass--energy relation $μ_s=ω$ turns this into the bound $\tilde{q}_s/μ_s>r_{\min}/\tilde{Q}$. 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--Nordström 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.
Comments36 pages, 13 figures
