发表机构
Indian Institute of Technology Kanpur; Tianjin University（坎普尔印度理工学院; 天津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出鞍点阶命题，统一描述约化黑洞系综中系综平均广义自由能的涨落，揭示临界点由四次软模控制并给出四分之一温度贡献，且通过RN-AdS和Kerr-AdS黑洞解析验证其普适性。
AI 中文摘要
我们在约化欧几里得黑洞系综中，为系综平均广义自由能建立了鞍点阶命题。在正则性和稳定性假设下，主导涨落贡献由主导鞍点周围第一个稳定项的阶数决定。普通临界点由四次软模控制，给出四分之一温度贡献，而非常见的半温度高斯结果。我们在四维RN-AdS和Kerr-AdS黑洞中解析验证了这一点，并将其热力学控制映射到公共四次规范型，其标度函数沿零场单阱方向连接临界区和高斯区。该命题还扩展到具有加权齐次主导势的耦合集体模。这些结果为通过黑洞临界性统一描述约化系综涨落提供了框架。
英文摘要
We establish a saddle-order proposition for the ensemble-averaged generalized free energy in reduced Euclidean black hole ensembles. Under regularity and stability assumptions, the leading fluctuation contribution is determined by the order of the first stabilizing term around the dominant saddle. An ordinary critical point is governed by a quartic soft mode, giving a quarter-temperature contribution instead of the familiar half-temperature Gaussian result. We verify this analytically for four-dimensional RN-AdS and Kerr-AdS black holes and map their thermodynamic controls to a common quartic normal form, whose scaling function connects the critical and Gaussian regimes along the zero-field one-well direction. The proposition also extends to coupled collective modes with weighted-homogeneous leading potentials. These results provide a unified description of reduced-ensemble fluctuations through black hole criticality.
Comments14 pages
