发表机构
Guangzhou City University of Technology（广州城市理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从熵泛函推导爱因斯坦方程，并用视界留数构造Wald熵，重现Schwarzschild结果，同时揭示极点与动力学等同的局限，为引力热力学提供一致性检验。
AI 中文摘要
引力的热力学描述既涉及时空动力学的变分条件，也涉及与视界相关的解析结构。我们在保持各自假设不同的前提下考察它们之间的关系。首先，我们从已确立的零向量熵泛函出发，给出了爱因斯坦方程的显式推导，包括零约束、物质项以及与宇宙学常数相关的积分常数。其次，对于具有非简并 Killing 视界的解析静态球对称几何，我们定义了一个亚纯径向一次形式，其留数等于表面重力倒数的一半。欧几里得正则性随后确定了霍金温度。将该留数与爱因斯坦-希尔伯特 Noether 荷相结合，可得到 Wald 熵的归一化围道表示。该构造重现了 Schwarzschild 温度、熵和 Smarr 关系，但并不构成面积定律的独立微观推导。我们确定了极点结构与动力学之间更强等同的局限：一个渐近平坦族可以保留 Schwarzschild 视界留数、面积、表面重力和质量，同时违反真空爱因斯坦方程，而一个极端带电解则具有高阶极点。我们还证明了为何将未指定的熵泛函指数化不会产生普适的熵留数。由此得到的框架将熵平稳性、视界解析性和荷归一化分离开来，为引力奇点的进一步热力学解释提供了明确的一致性检验。
英文摘要
Thermodynamic descriptions of gravity involve both variational conditions for spacetime dynamics and analytic structures associated with horizons. We examine their relation while keeping their assumptions distinct. First, we present an explicit derivation of the Einstein equation from the established null-vector entropy functional, including the null constraint, the matter term, and the integration constant associated with the cosmological constant. Second, for an analytic static spherical geometry with a nondegenerate Killing horizon, we define a meromorphic radial one-form whose residue is the inverse of twice the surface gravity. Euclidean regularity then fixes the Hawking temperature. Combining this residue with the Einstein--Hilbert Noether charge gives a normalized contour representation of the Wald entropy. The construction reproduces the Schwarzschild temperature, entropy, and Smarr relation, but does not constitute an independent microscopic derivation of the area law. We establish the limits of a stronger identification between pole structure and dynamics: an asymptotically flat family can retain the Schwarzschild horizon residue, area, surface gravity, and mass while violating the vacuum Einstein equation, and an extremal charged solution possesses a higher-order pole. We also show why exponentiating an unspecified entropy functional does not produce a universal entropy residue. The resulting framework separates entropy stationarity, horizon analyticity, and charge normalization, providing explicit consistency tests for further thermodynamic interpretations of gravitational singularities.
