Can we know about black hole thermodynamics through shadows?
Xin-Chang Cai, Yan-Gang Miao
备注：
v1: 31 pages, 11 figures, a new paper regarding shadow and thermodynamics for both spherically symmetric and rotating black holes, substantial new results for rotating black holes, only a small part of discussions on shadow and scalar curvature for spherically symmetric black holes overlapping with arXiv:2101.10780; v4: clarifications added, typos corrected
We investigate the relationship between shadow radius and microstructure for a general static spherically symmetric black hole and confirm their close connection. In this regard, we take the Reissner-Nordström (AdS) black hole as an example to do the concrete analysis. On the other hand, we study for the Kerr (AdS) black hole the relationship between its shadow and thermodynamics in the aspects of phase transition and microstructure. Our results for the Kerr (AdS) black hole show that the shadow radius $r_{\rm sh}$, the deformation parameters $δ_s$ and $k_s$, and the circularity deviation $ΔC$ can reflect the black hole thermodynamics. In addition, we give the constraints to the relaxation time of the M$87^{*}$ black hole by combining its shadow data and the Bekenstein-Hod universal bounds when the M$87^{*}$ is regarded as the Reissner-Nordström or Kerr black hole. We predict that the minimum relaxation times of M$87^{*}$ black hole and Sgr $A^{*}$ black hole are approximately 3 days and 2.64 minutes, respectively. Finally, we draw the first graph of the minimum relaxation time $τ_{\rm min}$ with respect to the maximum shadow radius $ r_{\rm sh}^{\rm max}$ at different mass levels.
Gravity/thermodynamics correspondence via black hole shadows
Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University（兰州大学理论物理中心、甘肃省理论物理重点实验室、教育部量子理论与应用重点实验室、甘肃省量子物理学基础学科研究中心）
Probing Black Hole Thermodynamics and Microstructure via the Shadow of Sagittarius A*
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and Icra, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
Testing the Weak Gravity Conjecture via Gravitational Lensing, Black Hole Shadows, and Barrow Thermodynamics in F(R)-Euler-Heisenberg (A)dS Black Holes
Damghan University（达姆甘大学）；Eastern Mediterranean University（东地中海大学）；University of Mazandaran（马赞德兰大学）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Canadian Quantum Research Center（加拿大量子研究中心）；Khazar University（哈扎尔大学）
Shadow of rotating black holes with consistent thermodynamics
RIKEN iTHEMS（理化学研究所 iTHEMS）；Department of Physics, National Central University（中央大学物理系）；Center for High Energy and High Field Physics (CHiP), National Central University（中央大学高能高场物理中心 (CHiP)）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心 (APCTP)）；Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（大阪公立大学 南部阳一郎理论与实验物理研究所 (NITEP)）
Null Geodesics, Thermodynamics, Weak Gravitational Lensing, and Black Hole Shadow Characteristics of a Frolov Regular Black Hole with Constraints from EHT Observations
Naked Singularities and Black Hole Thermodynamics from Shadows and Photon Rings in the Quantum Oppenheimer-Snyder Model
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Fesenkov Astrophysical Institute（费森可夫天体物理研究所）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Università di Roma “La Sapienza”（罗马第一大学）
Geometrothermodynamics of Black Hole Shadows: A Review
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
研究了静态球对称黑洞的阴影半径（光球半径）与黑洞微结构之间的关系，证实了它们之间的密切联系。作为具体分析，我们以Reissner-Nordstr $\mathrm{\ddot{o}}$ m AdS黑洞被完全流体暗物质包围（RN AdS黑洞被PFDM包围）为例.我们计算了Ruppeiner热力学标量曲率和阴影半径（光球半径）的具体模型。一方面，我们发现理想流体暗物质的密度越大，使得黑洞分子更有可能具有吸引力的相互作用。另一方面，我们提供的支持，我们的一般调查，阴影半径（光球半径）确实连接这个模型的微观结构。
Black holes in general relativity coupled with NEDs surrounded by PFDM: thermodynamics, epicyclic oscillations, QPOs, and shadow
The Assam Royal Global University（阿萨姆皇家全球大学）；New Uzbekistan University（新乌兹别克斯坦大学）；Institute of Fundamental and Applied Research, National Research University TIIAME（基础与应用研究所，国立研究大学TIIAME）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）
Phase Transitions, Shadows, and Microstructure of Kerr-anti-de Sitter Black Holes from Geometrothermodynamics
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and Icra, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
Optical and Thermodynamic Properties of a Rotating Dyonic Black Hole Spacetime in $\mathcal{N} = 2, U(1)^2$ gauged supergravity
研究了在$\mathcal{N} = 2, U(1)^2$规范超引力中光子绕旋转双子黑洞的零测地线和最近距离。分析了不同黑洞参数下的黑洞阴影现象。此外，在视界处的各种热力学参数下，对该黑洞的各种热力学性质进行了研究。本文还研究了该黑洞时空热力学稳定性的热容。直观地研究了黑洞参数$ ν$、$ e $、$ ν$、$ g $和$N_{g}$的不同取值对黑洞阴影现象和热力学参数的影响。
Shadow and Thermodynamics of deformed Schwarzschild-AdS black hole with a Cloud of Strings embedded in Perfect Fluid Dark Matter
The Assam Royal Global University（阿萨姆皇家全球大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Università di Roma “La Sapienza”（罗马第一大学）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
Phase transitions, shadows, and microstructure of Reissner-Nordström-Anti-de-Sitter black holes from a geometrothermodynamic perspective
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and Icra, Università di Roma “La Sapienza”（罗马大学物理系与ICRA）；Al-Farabi Kazakh National University（阿尔-法拉比哈萨克国立大学）
GUP-corrected black holes: Thermodynamic properties, evaporation time and shadow constraint from EHT Observations of M87* and Sgr A*
Zunyi Normal University（遵义师范学院）；Huzhou University（湖州学院）；Instituto Politécnico Nacional（国立理工学院）；Lorestan University（洛雷斯坦大学）；University of Hradec Králové（赫拉德茨-克拉洛韦大学）；Universidad de Valladolid（巴利亚多利德大学）
Optical and thermodynamic properties of Kerr-Bertotti-Robinson black holes
California State University, Fresno（弗雷斯诺加州州立大学）；University of Hradec Králové（赫拉德茨克拉洛韦大学）；Khazar University（卡扎尔大学）；Nazarbayev University（纳扎尔巴耶夫大学）；National Taiwan University（台湾大学）；Arizona State University（亚利桑那州立大学）；University of Helsinki（赫尔辛基大学）；Università di Camerino（卡梅里诺大学）；University at Albany-SUNY（奥尔巴尼纽约州立大学）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所-布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Center for Theoretical Physics, Khazar University（卡扎尔大学理论物理中心）
Thermodynamics, thermodynamic geometry, and the shadow of a Bardeen black hole surrounded by a Kiselev fluid: the role of regularity, asymptotics, and observational self-consistency
Gravitational equal-area law and critical phenomena of cuspy black hole shadow
Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University（兰州大学）
