发表机构
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh; Saha Institute of Nuclear Physics; Department of Physics Indian Institute of Technology Kanpur（爱丁堡大学数学学院与麦克斯韦数学科学研究所; 萨哈核物理研究所; 坎普尔印度理工学院物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文比较了高阶导数引力中Wald熵的两种非稳态修正构造$S_\text{Wall}$与$S_\text{dyn}$的差异，开发了从$S_\text{dyn}$推导$S_\text{Wall}$的算法，并以黎曼平方引力为例验证结果。
AI 中文摘要
在本研究中，我们分析了两种近期构造的异同，这两种构造在将稳态黑洞的Wald熵推广到一般高阶导数引力的非稳态情形时采用了不同的方法。其中一种记为$S_\text{Wall}$，通过利用近地平线几何的boost对称性构造而成；另一种记为$S_\text{dyn}$，则基于Wald-Iyer诺特定荷形式论，通过协变相空间分析得到。$S_\text{dyn}$在构造上仅定义于稳态黑洞解附近的线性化涨落，而$S_\text{Wall}$的构造无需此类线性化。尽管要将$S_\text{Wall}$解释为良定义的熵概念必须进行线性化，但其构造本身自然包含动力学涨落的高阶项。通过比较两种构造的底层技术结构，我们阐明了它们所基于方法的根本差异。我们证明，在给定$S_\text{Wall}$的前提下构造$S_\text{dyn}$是直接的，反之则更为复杂。我们开发了一种算法，在满足特定技术条件的情况下，从一般微分同胚不变引力理论中$S_\text{dyn}$的已知表达式，得到$S_\text{Wall}$的局域表达式。我们通过高阶导数引力的黎曼平方这一具体案例的明确演示，验证了我们的分析结果。
英文摘要
In this work, we analyze the differences and similarities between two recent constructions, which are distinct in their methodologies for extending the Wald entropy of stationary black holes to non-stationary situations in general higher-derivative gravity. One of them, denoted by $S_\text{Wall}$, is constructed by exploiting the boost symmetry of the near-horizon geometry, whereas the other, denoted by $S_\text{dyn}$, is obtained from a covariant phase-space analysis based on the Wald-Iyer Noether charge formalism. While $S_\text{dyn}$ is, by construction, defined only for linearized fluctuations around a stationary black hole solution, $S_\text{Wall}$ does not require such a linearization for its construction. Although the linearization is necessary to interpret $S_\text{Wall}$ as a well-defined notion of entropy, the construction itself naturally contains terms that are higher order in the dynamical fluctuations. By comparing the technical structures underlying the two constructions, we clarify the fundamental differences between the methods on which they are based. We demonstrate that while the construction of $S_\text{dyn}$ given the $S_\text{Wall}$ is straightforward, the converse is more subtle. We develop an algorithm to obtain a local expression for $S_\text{Wall}$ from a known expression for $S_\text{dyn}$ in a generic diffeomorphism-invariant theory of gravity, provided certain technical conditions are satisfied. We justify our analytical findings with explicit demonstrations in a particular case: the Riemann-squared example of the higher-derivative theory of gravity.
Comments18 pages + appendices; V2: minor typos fixed, references updated
