We study the phase transition of a regular Hayward-AdS black hole by introducing a new order parameter, the potential conjugate to the magnetic charge due to the non-linearly coupled electromagnetic field. We use Landau continuous phase transition theory to discuss the van der Waals like critical phenomena of the black hole. The popular interpretation of the AdS black hole phase transition as between a large and a small black hole is reinterpreted as the transition between a high potential phase and a low potential phase. The underlying microstructure for this phase transition is probed using the Ruppeiner geometry. By investigating the behaviour of the Ruppeiner scalar curvature, we find that the charged and uncharged (effective) molecules of the black hole have distinct microstructures analogous to fermion and boson gas.
We study the interaction between the microstructures of Hayward-AdS black hole using Ruppeiner geometry. Our investigation shows that the dominant interaction between the black hole molecules is attractive in most part of the parametric space of temperature and volume, as in van der Waals system. However, in contrast to the van der Waals fluid, there exists a weak dominant repulsive interaction for small black hole phase in some parameter range. This result clearly distinguishes the interactions in a magnetically charged black hole from that of van der Waals fluid. However, these sort of inter…
Motivated by recent work on rotating black hole shadow [Phys. Rev. D101, 084029 (2020)], we investigate the shadow behaviors of rotating Hayward-de Sitter black hole for static observers at a finite distance in terms of astronomical observables. This paper uses the newly introduced distortion parameter in [arXiv:2006.00685] to describe the shadow's shape quantitatively. We show that the spin parameter would distort shadows and the magnetic monopole charge would increase the degree of deformation. At the same time, the distortion could be relieved because of the cosmological constant and the di…
In this paper, we attempt to further study the heat engine efficiency for the regular black hole (BH) with an anti-de Sitter (AdS) background where the working material is the Hayward-AdS (HAdS) BH. In the extended phase space, we investigate the heat engine efficiency of the HAdS BH by defining the cosmological constant as the thermodynamic pressure $P$ and deriving the mechanical work from the $PdV$ terms. Then, we obtain the relation between the efficiency and the entropy/pressure and plot these function figures. Meanwhile, we compare the relation between the HAdS BH with that of the Bardee…
In this article, we analytically investigate the microstructure of a five-dimensional neutral Gauss-Bonnet black hole, in the background of anti-de Sitter spacetime, using scalar curvature of the Ruppeiner geometry constructed via adiabatic compressibility. The microstructure details associated with the small-large black hole phase transition are probed in the parameter space of pressure and volume. The curvature scalar shows similar properties for both phases of the black hole, it diverges in the vicinity of critical point and approaches zero for extremal black holes. We show that the dominan…
We study the phase structure and the microscopic interactions in regular Bardeen AdS black hole. The stable and metastable phases in the black hole are analysed through coexistence and spinodal curves. The solutions are obtained numerically as the analytic solution to the coexistence curve is not feasible. The $P_r-T_r$ coexistence equation is obtained using a fitting formula. The coexistence and spinodal curves are plotted in $P_r-T_r$ and $T_r-V_r$ planes to explore the phase structure of the black hole. In the second part of our study, we were able to probe the microscopic interactions of r…
The Ruppeiner geometry of thermodynamic fluctuations provides a powerful diagnostic of black hole microstructures. We investigate this for charged AdS black holes and find that while an attractive microstructure interaction dominates for most parameter ranges, a weak repulsive interaction dominates for small black holes of high temperature. This unique property distinguishes the black hole system from that of a Van der Waals fluid, where only attractive microstructure interactions are found. We also find two other novel universal properties for charged black holes. One is that the repulsive in…
Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the …
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）
$P$--$V$ criticality, Joule--Thomson expansion, and holographic heat engine of charged Hayward-AdS black holes with a cloud of strings and perfect fluid dark matter
We describe two different, but equivalent semiclassical views of black hole physics in which the equivalence principle and unitarity are both accommodated. In one, unitarity is built-in, while the black hole interior emerges only effectively as a collective phenomenon involving horizon (and possibly other) degrees of freedom. In the other, more widely studied approach, the existence of the interior is manifest, while the unitarity of the underlying dynamics can be captured only indirectly by incorporating certain nonperturbative effects of gravity. These two pictures correspond to a distant de…
We suggest a new thermodynamic curvature, constructed via adiabatic compressibility, for examining the internal microstructure of charged black holes in an anti-de Sitter (AdS) background. We analyze the microscopic properties of small-large phase transition of black holes with pressure and volume as the fluctuation variables. We observe that strong repulsive interactions dominate among the micro-structures of near extremal small black holes, and the thermodynamic curvature diverges to positive infinity for the extremal black holes. At the critical point, however, thermodynamic curvature diver…
Combining with the small-large black hole phase transition, the thermodynamic geometry has been well applied to study the microstructure for the charged AdS black hole. In this paper, we extend the geometric approach to the rotating Kerr-AdS black hole and aim to develop a general approach for the Kerr-AdS black hole. Treating the entropy and pressure as the fluctuation coordinates, we construct the Ruppeiner geometry for the Kerr-AdS black hole by making the use of the Christodoulou-Ruffini-like squared-mass formula, which is quite different from the charged case. Employing the empirical obse…
Our aim is studying the thermodynamics of cosmological models including initial and final de-Sitter eras. For this propose, bearing Cai-Kim temperature in mind, we investigate the thermodynamic properties of a dark energy candidate with variable energy density, and show that the state parameter of this dark energy candidate should obey the $ω_D\neq-1$ constraint, whiles there is no interaction between the fluids filled the universe, and the universe is not in the de-Sitter eras. Additionally, based on thermal fluctuation theory, we study the possibility of inducing fluctuations to the entropy …
By treating black hole as the macroscopic stable state on the free energy landscape, we propose that the stochastic dynamics of the black hole phase transition can be effectively described by the Langevin equation or equivalently by the Fokker-Planck equation in phase space. We demonstrate the turnover of the kinetics for the charged anti-de Sitter black hole phase transition, which shows that the mean first passage time is linear with the friction in the high damping regime and inversely proportional to the friction in the low damping regime. The fluctuations in the kinetics are shown to be l…
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）
We provide a new five dimensional black string--like solution by means of the embedding of a four dimensional regular black hole into a compact extra dimension. We enunciate a list of constraints in order to that the five dimensional black string--like solution to be regular, and, following these constraints we construct our solution. Instead of the usual singularity, it is formed a core whose topology corresponds to the product between the de--Sitter core of the four dimensional Hayward solution and $S^1$. The horizon has topology $S^2 \times S^1$. At infinity of the radial coordinate the reg…
In recent years, the thermodynamic properties of black holes are topics of interests. We investigate the thermodynamic properties like surface gravity and Hawking temperature on event horizon of regular black holes viz. {\it Hayward Class} and {\it asymptotically AdS (Anti-de Sitter)} black holes. We also analyze the {\it thermodynamic volume} and {\it naive geometric volume} of asymptotically AdS black holes and show that the entropy of these black holes is simply the ratio of the naive geometric volume to thermodynamic volume. We plot the different graphs and interpret them physically. We de…
Standard models of "regular black holes" typically have asymptotically de Sitter regions at their cores. Herein we shall consider novel "hollow" regular black holes, those with asymptotically Minkowski cores. The reason for doing so is twofold: First, these models greatly simplify the physics in the deep core, and second, one can trade off rather messy cubic and quartic polynomial equations for somewhat more elegant special functions such as exponentials and the increasingly important Lambert $W$ function. While these "hollow" regular black holes share many features with the Bardeen/Hayward/Fr…
We investigate the shadow cast by a sort of new regular black holes which are characterized by an asymptotically Minkowski core and the Sub-Planckian curvature. Firstly, we extend the metric with spherical symmetry to the one of rotating Kerr-like black holes and derive the null geodesics with circular orbit near the horizon of the black hole, and then plot the shadow of black holes with different values of the deviation parameter. It is found that the size of the shadow shrinks with the increase of the deviation parameter, while the shape of the shadow becomes more deformed. In particular, by…
Pontificia Universidad Javeriana（波哥大耶稣会天主教大学）；ICTP–South American Institute for Fundamental Research（国际理论物理中心南美基础研究所）；Universidade Federal de São Paulo (UNIFESP)（圣保罗联邦大学）
Employing the free energy landscape, we study the phase transition and its dynamics for a class of regular black holes in Anti-de Sitter spacetime governed by the coupling of non-linear electrodynamics, which reduces to Hayward and Bardeen solutions for particular values of spacetime parameters. The Fokker-Planck equation is solved numerically by imposing the reflecting boundary condition and a suitable initial condition, using which, we investigate the probabilistic evolution of regular AdS black holes. In this approach, the on-shell Gibbs free energy is treated as a function of the radius of…
We introduce a new microscopic quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic quantity is proportional to the macroscopic quantity -- entropy surface density $σ_{S}$, thus connecting a microscopic quantity to a macroscopic quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) tha…
Ruppeiner geometry has been found to be a novel promising approach to uncover the microstructure of fluid systems and black holes. In this work, combining with the micro model of the Van der Waals fluid, we shall propose a first microscopic interpretation for the empirical observation of Ruppeiner geometry. Then employing the microscopic interpretation, we disclose the potential microstructure for the anti-de Sitter black hole systems. Of particular interest, we obtain the microscopic interaction potentials for the underlying black hole molecules. This significantly strengthens the study towar…
We develop the regular black hole solutions recently proposed in arXiv:2109.05974 by incorporating the 1-loop quantum correction to the Newton potential as well as a time delay between an observer at the regular center and that at infinity. We define the maximal time delay between the center and the infinity by scanning the mass of black holes such that the sub-Planckian feature of Kretschmann scalar curvature is preserved during the whole process of evaporation. We also compare the distinct behavior of Kretschmann curvature for black holes with an asymptotically Minkowski core and those with …
Black holes are among the most fascinating objects populating our universe. Their characteristic features, encompassing spacetime singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. In this note we observe that the renormalization group improved Schwarzschild black holes constructed by Bonanno and Reuter within Weinberg's asymptotic safety program constitute a prototypical example of a Hayward geometry used to model non-singular black holes within quantum gravity phenomenology. Moreover, they share many features of a Planck sta…
In this paper, we construct a class of charged and regular black hole solutions in Verlinde's Emergent Gravity (VEG). In particular, these solutions include, black holes with asymptotically Minkowski core, T-duality, Frolov/Simpson-Visser type solutions, as well as the Bardeen/Hayward type solutions as a special case. Using the relation between the apparent dark matter and the baryonic matter we find the effect of apparent dark matter on the spacetime geometry. We show that in general, the apparent dark matter leads to non-asymptotically flat spacetime geometry and, in the special limit of a p…
Taking the quantum electrodynamics (QED) effect into account, we study the black hole phase transition and Ruppeiner geometry for the Euler-Heisenberg anti-de Sitter black hole in the extended phase space. For negative and small positive QED parameter, we observe a small/large black hole phase transition and reentrant phase transition, respectively. While a large positive value of the QED parameter ruins the phase transition. The phase diagrams for each case are explicitly exhibited. Then we construct the Ruppeiner geometry in the thermodynamic parameter space. Different features of the corres…
In this paper, we study the phase structure and equilibrium state space geometry of charged topological Gauss-Bonnet black holes in $d$-dimensional anti-de Sitter spacetime. Several critical points are obtained in the canonical ensemble, and the critical phenomena and critical exponents near them are examined. We find that the phase structures and critical phenomena drastically depend on the cosmological constant $Λ$ and dimensionality $d$. The result also shows that there exists an analogy between the black hole and the van der Waals liquid gas system. Moreover, we explore the phase transitio…
