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）
The shadow of a black hole serves as a pristine window into the strong-gravity regime, with cuspy feature emerging as a smoking-gun signature of physics beyond the Kerr paradigm. In this paper, we extend the work of [arXiv:2601.15612 [gr-qc]] and study the detailed properties of the cuspy shadow by using the parametric expressions of the shadow boundary. From a topological perspective, we provide a rigorous topological classification of these shadows, categorizing them into distinct ``rectangular" and ``8-shape" topologies. Crucially, we establish a formal gravity/thermodynamics correspondence by mapping the cuspy shadow to the swallowtail behavior observed in thermodynamic free energy. We demonstrate that the self-intersection of the shadow boundary, marking a geometric phase transition, can be precisely determined through three independent but equivalently thermodynamic-like approaches. Furthermore, we analytically derive the critical exponents governing the emergence of these cusps, revealing that they are consistent with the mean-field universality class. Our results suggest that the observational features of black hole shadows are deeply rooted in the underlying gravitational thermodynamics, offering a novel framework to probe the fundamental nature of spacetime.
We consider the equivalence of quasinormal modes and geodesic quantities recently brought back due to the black hole shadow observation by Event Horizon Telescope. Using WKB method we found an analytical relation between the real part of quasinormal frequencies at the eikonal limit and black hole shadow radius. We verify this correspondence with two black hole families in $4$ and $D$ dimensions, respectively.
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein-Gauss-Bonnet black hole. The perturbation of a massless scalar field in the black hole's background is adopted. The quasinormal modes are gotten by the $6th$ order WKB approximation approach and shadow radius, respectively. When the value of the Gauss-Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increase…
Null geodesics, quasinormal modes of a massless scalar field perturbation and the correspondence with shadow radii are investigated in the background spacetime of high-dimensional Einstein-Yang-Mills black holes. Based on the properties of null geodesics, we obtain the connection between the radius of a photon sphere and the radius of a horizon in the five- and six-dimensional Einstein-Yang-Mills spacetimes. Especially in the five-dimensional case, there exist two branches for the radius of a photon sphere, but only the branch outside the event horizon satisfies the condition of circular null …
In this paper we study the correspondence between the real part of quasinormal modes (QNMs) and the shadow radius in a wormhole spacetime. Firstly we consider the above correspondence in a static and spherically symmetric wormhole spacetime and then explore this correspondence numerically by considering different wormhole models having specific redshift functions. To this end, we generalize this correspondence to the rotation wormhole spacetime and calculate the typical shadow radius of the rotating wormhole when viewed from the equatorial plane. We argue that due to the rotation and depending…
We construct an exact black hole solution for the Einstein gravity coupled with the nonlinear electrodynamics (which corresponds to the Maxwell electrodynamics in the weak field limit) in the presence of a cloud of strings as the source. We study the thermodynamical properties of the black hole solutions and derive the corrected first-law of thermodynamics. The presence of a cloud of strings does not affect the stability of the present black hole. However, a second-order phase transition exists for this system at a critical horizon radius. Furthermore, we study the quasinormal modes and their …
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 $ΔC$…
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a charged black hole in presence of quintessence. The result shows that the shadow radius decreases with the increase of the electric charge. The quasinormal modes are derived by the sixth WKB approximation method and shadow radius, respectively. For the fixed electric charge and multipole number, the values of the real and imaginary parts of the quasinormal modes decrease with the increase of the quintessence charge. When the value of the multipole number is large, the quasinormal modes derived by the two …
In this paper, we consider the Einstein-massive gravity coupled to the Yang-Mills gauge field in five dimensions. Concentrating on the static solutions with planar horizon geometry, we explore the thermodynamic behavior in the extended phase space and examine the validity of the first law of thermodynamics besides local thermal stability by the Hessian matrix. We observe that although the topology of boundary is planar, there exists the van der Waals like phase transition for this kind of solution. We find the critical quantities and discuss how the massive and Yang-Mills parameters affect the…
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a $4$-dimensional black hole with a deficit solid angle and quintessence-like matter. We find that the radii of the photon sphere and shadow decrease with the decreases of the deficit solid angle and density of quintessence-like matter. The quasinormal modes are gotten by the sixth order WKB approximation method and shadow radius, respectively. The values of the real part and imaginary parts of the quasinormal modes increase with the decrease of the values of the deficit solid angle and density of quintesse…
We investigate the relations between the black hole shadow and charged AdS black hole critical behaviour in the extended phase space. Using the thermo-shadow formalism built-in [1], we reveal that the shadow radius can be considered as an efficient tool to study thermodynamical black hole systems. Based on such arguments, we build a thermal profile by varying the RN-AdS black hole temperature on the shadow silhouette. Among others, the Van der Waals-like phase transition takes place. This could open a new window on the thermal picture of black holes and the corresponding thermodynamics from th…
The dependence of the black hole (BH) shadow and thermodynamics may be structured in the regular spacetime. Taking the regular Bardeen-AdS BH as an example, the relationship between the shadow radius and the event horizon radius is derived. It is found that these two radii display a positive correlation, implying that the BH temperature can be rewritten as a function of shadow radius in the regular spacetime. By analyzing the phase transition curves under the shadow context, we found that the shadow radius can replace the event horizon radius to present the BH phase transition process, and the…
We find an exact black hole solution with a minimally coupled scalar field. The corresponding spacetime has two horizons and one of the them is the black hole event horizon and the other is the cosmic horizon. In this sense, the solution is analogous to the Schwarzschild-de Sitter (or anti-de Sitter) spacetime. We investigate the thermodynamics and construct the first law of thermodynamics. At the same time, we make a study on the shadow and quasinormal modes of this black hole solution.
The relation between the black hole shadow and the black hole thermodynamics is investigated. We find that the phase structure can be reflected by the shadow radius for the spherically symmetric black hole. We also find that the shadow size gives correct information but the distortion of the shadow gives wrong information of the phase structure for the axially symmetric black hole.
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
In this paper, a preliminary correspondence between the thermodynamic curvature and the isoperimetric theorem is established from a $4$-dimensional ultraspinning black hole. We find that the thermodynamic curvature of ultraspinning black hole is negative which means the ultraspinning black hole is likely to present an attractive between its molecules phenomenologically if we accept the analogical observation that the thermodynamic curvature reflects the interaction between molecules in a black hole system. Meanwhile we obtain a general conclusion that the thermodynamic curvature of the extreme…
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）
We investigate the relationship between shadow radii (photosphere radii) and black hole microstructures for a static spherically symmetric black hole and confirm their close connection. As a concrete analysis, we take the Reissner-Nordstr$\mathrm{\ddot{o}}$m AdS black hole surrounded by perfect fluid dark matter (RN AdS black hole surrounded by PFDM) as an example. We calculate the Ruppeiner thermodynamic scalar curvature and shadow radius (photosphere radius) for the specific model. On the one hand, we find that the greater density of the perfect fluid dark matter makes black hole molecules m…
We study the thermodynamical aspects of $f(R)$ gravity in the Jordan and the Einstein frame, and we investigate the corresponding equivalence of the thermodynamical quantities in the two frames. We examine static spherically symmetric black hole solutions with constant Ricci scalar curvature $R$, and as we demonstrate, the thermodynamical quantities in the two frames are equivalent. However, for the case of black holes with non-constant scalar curvature $R$, the thermodynamical equivalence of the two frames is no longer valid. In addition, we examine cosmological solutions with non-trivial cur…
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）
We speculate on various thermodynamic features of the inner horizon~(${\mathcal H}^{-}$) and outer horizons~(${\mathcal H}^{+}$) of Kehagias-Sfetsos~(KS) black hole~(BH) in the background of Hořava Lifshitz gravity. We compute particularly the \emph{area product, area sum, area minus and area division} of the BH horizons. We find that they all are \emph{not} showing universal behavior whereas the product is a universal quantity~ [Pradhan P., \textit{Phys. Lett. B}, {\bf 747} (2015) {64}]. Based on these relations, we derive the area bound of all horizons. From the area bound we derive the entr…
