热力学几何作为缺失环节：迈向黑洞一级相变的统一框架
Thermodynamic geometry as the missing link: toward a unified framework for black hole first-order phase transitions
浏览论文内容
中文总结 AI 辅助
本研究证明热力学几何发散点与温度函数临界条件等价，并将其纳入统一框架，从而统一四种黑洞一级相变描述方法。
中文摘要 AI 辅助
黑洞一级相变已被若干看似独立的框架所描述，包括局部几何、全局拓扑、复分析和热力学几何。虽然前三种已被统一，但热力学几何仍处于其外。我们证明了归一化Ruppeiner曲率标量$R_N$的发散点与$T'(r_h)=0$的解完全重合，其中$r_h$为视界半径。这些解包括极值点（旋节线点）和驻拐点（热力学临界点）。因此，$R_N$的发散是一级相变的必要但不充分条件。这阐明了曲率发散的数学起源，以及为何热力学几何能可靠地指示但无法单独确认相变。以局部几何框架作为中心框架，我们将Ruppeiner几何纳入这一统一图景；类似的分析也适用于Weinhold几何。因此，四个框架在基于温度函数局部折叠的单一结构中得以统一。这增进了我们对黑洞一级相变数学结构的理解，并为可能扩展到其他类型相变提供了线索。
英文摘要
Black hole first-order phase transitions have been described by several seemingly independent frameworks, including local geometry, global topology, complex analysis, and thermodynamic geometry. While the first three have been unified, thermodynamic geometry has remained outside. We prove that the divergence points of the normalized Ruppeiner curvature scalar $R_N$ coincide exactly with the solutions of $T'(r_h)=0$, where $r_h$ is the horizon radius. These solutions include extremal points (spinodal points) and stationary inflection points (thermodynamic critical points). Thus, the divergence of $R_N$ is a necessary but not sufficient condition for a first-order phase transition. This clarifies the mathematical origin of curvature divergence and why thermodynamic geometry can reliably indicate but not alone confirm phase transitions. Using the local geometric framework as a central framework, we incorporate Ruppeiner geometry into this unified picture; a similar analysis also applies to Weinhold geometry. Consequently, the four frameworks are unified within a single structure based on the local folding of the temperature function. This advances our understanding of the mathematical structure of black hole first-order phase transitions and provides clues for possible extensions to other types of phase transitions.
发表机构
- Northeastern University（东北大学）
机构由 AI 辅助整理，请以论文原文为准。
