发表机构
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México; Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”; Al-Farabi Kazakh National University（墨西哥国立自治大学核科学研究所; 罗马第一大学物理系及ICRA; 阿尔法拉比哈萨克国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文综述黑洞阴影与几何热力学（GTD）的对应关系，针对三类黑洞分析其热力学结构与阴影构型的映射，提出雅可比秩判据，以人马座A*为例说明阴影观测可约束热力学态并区分GTD度规结构。
AI 中文摘要
黑洞阴影与几何热力学（GTD）虽定义于不同空间，但依赖相同的宏观黑洞参数。本文综述了雷斯纳-诺德斯特龙（RN）黑洞、克尔（Kerr）黑洞及克尔-反德西特（Kerr-AdS）黑洞的对应关系：三种GTD度规呈现互补的热力学结构，包括戴维斯不稳定性、极端与简并极限、正则曲率零点，可映射至阴影构型；克尔-AdS还将该对应关系拓展至非对称阴影与多维平衡态。我们提出从阴影观测量进行热力学重构的局部雅可比秩判据，并讨论阴影-微观结构（SM）图作为GTD分类平衡态的光学表征；对人马座A*的应用阐释了逆问题：阴影观测可约束热力学态，为识别可区分GTD度规结构的其他度规依赖观测量提供基础。
英文摘要
Black-hole shadows and geometrothermodynamics (GTD) are defined in different spaces but depend on the same macroscopic black-hole parameters. We review their correspondence for Reissner--Nordström (RN), Kerr, and Kerr--AdS black holes. The three GTD metrics reveal complementary thermodynamic structures, including Davies instabilities, extremal and degenerate limits, and regular curvature zeros, which can be mapped to shadow configurations. Kerr--AdS extends this correspondence to asymmetric shadows and multidimensional equilibrium states. We formulate a local Jacobian-rank criterion for thermodynamic reconstruction from shadow observables and discuss shadow--microstructure (SM) diagrams as optical representations of GTD-classified equilibrium states. The application to Sagittarius A* illustrates the inverse problem: shadow observations constrain thermodynamic states and provide a basis for identifying additional metric-dependent observables that could distinguish among the GTD metric structures.
CommentsPrepare for Entropy's Special Issue on New Advances in Black Hole Thermodynamics
