arXiv subjects

Zhen-Ming Xu

Publications and source records attributed to Zhen-Ming Xu.

At least 19 recordsLinked to original sources

arXiv2026

Complex Plane Phase Diagram and Widom Line for the Born-Infeld Black Holes with Reentrant Phase Transition

The Lee-Yang phase transition theory applied in the anti-de Sitter (AdS) black hole has inspired the exploration of complex phase diagram and supercritical phenomena in black hole thermodynamics. In this study, we extend the approach to the four dimensional Born-Infeld AdS black hole. This system exhibits a rich phase structure, including reentrant phase transitions, due to the modulation of the Born-Infeld nonlinear parameter. Through the Lee-Yang zeros, we obtained the complex phase diagram of the Born-Infeld AdS black hole and derived the supercritical crossover line -- Widom line, which strictly originates from the first-order stable critical point. The results indicate that Born-Infeld nonlinear effects significantly alter the types and characteristics of phase transition in critical region, while do not disrupt the uniqueness of the Widom line in supercritical region. Our study uncovers a universal simplified feature of the thermodynamic behavior of nonlinear gravitational systems in supercritical region. It also deepens our understanding of the fundamental connection between critical phenomena and continuous phase transitions in the extended phase space of black holes.

hep-th↗

arXiv2026

Mean first passage time and the Kramers escape rate of phase transitions for the Bardeen-AdS-class black hole

In this study, by utilizing the constructed generalized free energy alongside the Mean First-Passage Time and the Kramers escape rate from stochastic dynamics, we have obtained a comprehensive landscape of the phase transitions for the Bardeen-AdS-class black hole. This black hole model admits two distinct categories of solutions. Type I black holes feature a regular black hole solution, and Type II black holes possess a vacuum state solution. In the phase transition between the small black hole and the large black hole for Type I, the process may pass through a stable, metastable, or unstable regular black hole as an intermediate state. In contrast, for Type II black holes, the phase transition occurs exclusively between the vacuum state and the small black hole, and the transition process does not involve any regular black hole intermediate states.

gr-qc↗

arXiv2026

Thermodynamic supercriticality and complex phase diagram for the AdS black hole

In this study, we extend the application of the Lee-Yang phase transition theorem to the realm of AdS black hole thermodynamics, thereby deriving a comprehensive complex phase diagram for such systems. Our research augments extant studies on black hole thermodynamic phase diagrams, particularly in the regime above the critical point, by delineating the Widom line of AdS black holes. This boundary segregates the supercritical domain of the phase diagram into two disparate zones. As the system traverses the thermodynamic crossover within the supercritical region, it undergoes a transition from one supercritical phase to another, while maintaining the continuity of its thermodynamic state functions. This behavior is fundamentally different from that below the critical point, where crossing the coexistence line results in discontinuities of thermodynamic state functions. The Widom line enables a thermodynamic crossover between single-phase states without traversing the spinodal that emerges in the critical region.

gr-qc↗

arXiv2025

Thermodynamic supercriticality and complex phase diagram for charged Gauss-Bonnet AdS black holes

Lee-Yang zero theory plays a crucial role in phase transition theory and is widely employed in the critical behavior of statistical thermodynamics. The supercritical regime of black hole thermodynamics remains a relatively unexplored area, and recent applications of this theory to charged anti-de Sitter (AdS) black holes have initiated probes into this regime, revealing a simple structure partitioned by a single Widom line. In this paper, we apply Lee-Yang theory to charged Gauss-Bonnet AdS black holes, which feature complex phase diagrams (e.g., triple points), to determine how such structures are reflected in the supercritical regime. Notably, we observe a key dimensional difference in that the five-dimensional (5d) system, which lacks a triple point, confirms the known single Widom line structure, while the six-dimensional (6d) system, which admits a triple point, generates two distinct Widom lines. These lines partition the supercritical domain into three sectors (small-, intermediate-, and large- black hole-like phases), corresponding to the three phases coexisting at the triple point. Our results reveal a direct correspondence between the number of coexisting phases at a triple point and the number of distinct supercritical sectors separated by Widom lines.

hep-th↗

arXiv2025

Black hole thermodynamics from Iyer-Wald formalism with variable Newton's constant

Recent advances in black hole thermodynamics have intensified efforts to investigate its thermodynamic framework analogues to that of classical thermal systems. Departing from the extended phase space approach which involves a variable cosmological constant, the restricted phase space formalism focusing on the variations of Newton's gravitational constant in black hole thermodynamics is proposed. This approach enables the construction of a self-consistent thermodynamic structure that features both the first law and the Euler relation. In this paper, we demonstrate that for any diffeomorphism-invariant gravitational theory, the Iyer-Wald formalism is applicable to restricted phase space thermodynamics and construct a self-consistent extensive black hole thermodynamic system. Our work thereby establishes the Iyer-Wald approach as the geometric foundation for restricted phase space black hole thermodynamics.

gr-qc↗

arXiv2025

The Kramers escape rate of phase transitions for the 6-dimensional Gauss-Bonnet AdS black hole with triple phases

In this study, we obtain specific picture of the phase transitions for the 6-dimensional Gauss-Bonnet Anti-de Sitter (AdS) black hole with triple phases, using the generalized free energy we constructed and Kramers escape rate in stochastic motion. There are six possible phase transition processes between the three different stable states (small, medium, and large black hole states). During these phase transitions, there are two key temperatures. One is the temperature at which the medium black hole state emerges, and the other is the temperature at which the small black hole state annihilates. Meanwhile, two dynamic equilibrium processes are formed. One is a dynamic equilibrium of the transition from the medium black hole state to the large black hole state and the transition from the small black hole state to the medium black hole state. The other is a dynamic equilibrium of the transition from the small black hole state to the medium black hole state and the transition from the medium black hole state to the small black hole state.

gr-qc↗

arXiv2024

Thermodynamic bounce effect in quantum BTZ black hole

A novel thermodynamic phenomenon has been observed in the quantum Bañados-Teitelboim-Zanelli (qBTZ) black hole, utilizing generalized free energy and Kramer escape rate. This phenomenon also reveals the unique property of the quantum black hole. The stochastic thermal motion of various thermodynamic states within the black hole system induces phase transitions, under the influence of generalized free energy which obtained by extending Maxwell's construction. Through the analysis of Kramer escape rate, it is discovered that the qBTZ black hole thermodynamic system exhibits a bounce effect. It originates from the non-monotonicity of entropy in black hole thermodynamic systems. Furthermore, the overall thermodynamic picture of the qBTZ black hole has been obtained under different quantum backreactions.

gr-qc↗

arXiv2024

Generalized Maxwell equal area law and black holes in complex free energy

Maxwell equal area law is an important and traditional analytical tool in thermodynamic phase transition, especially in the calculation of gas-liquid phase transition, which reconciles the theoretical calculation with the experimental results. Undoubtedly, its importance is also self-evident for the black hole thermodynamic system. In this study, we construct a generalized Maxwell equal area law, which allows different states of thermodynamic systems to be within the generalized free energy. The black hole thermodynamic characteristics are spontaneously emerged in the free energy landscape. Furthermore, by analytic continuation, we utilize the properties of analytical functions to investigate some universal characteristics of thermodynamic phase transitions in black holes, and preliminarily establish the counterpart of thermodynamic phase transitions in the complex domain.

gr-qc↗

arXiv2024

Thermodynamic phase transition rate for the third-order Lovelock black hole in diverse dimensions

The phase transition has always been a major focus in the study of black hole thermodynamics. This study employs the Kramer escape rate from stochastic processes to investigate the first-order phase transition strength between the large and small black hole states. The results indicate that the phase transition of the third-order Lovelock black holes exhibits significant asymmetric characteristics in diverse dimensions both in the hyperbolic and spherical topology, with an overall trend of the transition from large black holes to small black holes. Especially for the spherical topology, when the dimension is higher than seven, there exists a certain temperature beyond which a dynamic equilibrium is established for the phase transition. This study provides valuable insights into the first-order phase transition rate of black holes and enriches the understanding of black hole phase transitions.

gr-qc↗

arXiv2023

Thermodynamic phase transition and winding number for the third-order Lovelock black hole

Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system. In this study, the connection between the phase transition of a black hole and the winding number derived by the complex analysis is used to predict the type of the black hole phase transition. For the third-order Lovelock black holes, at the hyperbolic topology in any dimensions and the spherical topology in $7$ dimensions, we arrive at the winding numbers both are $W=3$ which predicts that the system will undergo both the first-order and second-order phase transitions. For the spherical topology in $7<d<12$ dimensions, the winding number is $W=4$ and the corresponding phase transition will occur in two situations: one with only pure second-order phase transition and the other with both first-order and second-order phase transitions. We further confirm the correctness and rationality of this prediction by placing the black hole thermodynamics system in the potential field.

gr-qc↗

arXiv2023

Rate of the phase transition for a charged anti-de Sitter black hole

Phase transition is a core content of black hole thermodynamics. This study adopted the Kramer's escape rate method for describing the Brownian motion of particles in an external field to investigate the intensity of the phase transition between small and large black hole states. Some existing studies mostly focused on the formal analysis of the thermodynamic phase transition of black holes, but they neglected the detailed description of the phase transition process. Our results show that the phase transition between small and large black holes for charged anti-de Sitter (AdS) black holes presents serious asymmetric features, and the overall process is dominated by the transition from a small black hole to a large black hole. This study filled a research gap of a stochastic process analysis on the issue of the first-order phase transition rate in the AdS black hole.

gr-qc↗

arXiv2022

Revisit on thermodynamics of BTZ black hole with variable Newton constant

The thermodynamics of the BTZ black holes are revisited with variable Newton constant. A new pair of conjugated variables, the central charge $C$ and the chemical potential $μ$, is introduced as thermodynamic variables. The first law of thermodynamics and the Euler relation, instead of the Smarr relation in the extended phase space formalism, are matched perfectly in this formalism. Compatible with standard extensive thermodynamics, the black hole mass is verified to be a first order homogeneous function of the related extensive variables, and restores the role of internal energy. In addition, the heat capacity has also resulted in a first order homogeneous function in this formalism as we expected, and an asymptotic behavior in high temperature limit is shown intriguingly. The non-negatively of heat capacity indicates that the rotating and charged BTZ black holes are thermodynamically stable.

gr-qc↗

arXiv2021

Fokker-Planck equation for black holes in thermal potential

We construct a kind of thermal potential and then put the black hole thermodynamic system in it. In this regard, some thermodynamic properties of the black hole are related to the geometric characteristics of the thermal potential. Driven by the intrinsic thermodynamic fluctuations, the behavior of the black hole in the thermal potential is stochastic. With the help of solving the Fokker-Planck equation analytically, we obtain the discrete energy spectrum of Schwarzschild and Banados-Teitelboim-Zanelli (BTZ) black holes in the thermal potential. For Schwarzschild black hole, the energy spectrum is proportional to the temperature of the ensemble, which is an external parameter, and the ground state is non-zero. For BTZ black hole, the energy spectrum only depends on the AdS radius, which is the intrinsic parameter. Moreover, the ground state of BTZ black hole in thermal potential is zero. This also reflects the difference between three-dimensional gravity and four-dimensional gravity.

gr-qc↗

arXiv2021

Thermodynamics curvature in phase transitions for AdS black hole

We investigate the thermodynamic curvature in the Hawking-Page phase transition and the second-order phase transition of the AdS black hole. It is shown that the thermodynamic curvature has the same behavior in these two different phase transitions. Specifically, the thermodynamic curvature in the Hawking-Page phase transition is the power function of the Hawking-Page phase transition temperature with exponent related to the spacetime dimension, or is invariably proportional to the reciprocal of the Hawking-Page phase transition entropy. For the thermodynamic curvature in the second-order phase transition, the conclusion is similar. The more enlightening result is that the ratio of thermodynamic curvatures along the two different phase transitions tends to the natural constant in the limit that the number of spacetime dimensions is infinite. The universal and novel result provides an essential difference between the Hawking-Page phase transition and the second-order phase transition of the AdS black hole in the large dimension paradigm.

gr-qc↗

arXiv2021

van der Waals fluid and charged AdS black hole in the Landau theory

By introducing the general construction of Landau functional of the van der Waals system and charged AdS black hole system, we have preliminarily realized the Landau continuous phase transition theory in black hole thermodynamics. The results show that the Landau functional constructed in present paper can directly reflect the physical process of black hole phase transition. Specifically, the splitting of the global minimum of the Landau functional corresponds to the second-order phase transition of the black hole, and the transformation of the global minimum reflects the first-order phase transition of the black hole.

gr-qc↗

arXiv2021

A shell of Bosons in Spherically Symmetric spacetimes

The thermodynamic properties of a shell of bosons with the inner surface locating at Planck length away from the horizon of Schwarzschild black holes by using statistical mechanics are studied. The covariant partition function of bosons is obtained, from which the Bose-Einstein condensation of bosons is found at a non-zero temperature in the curved spacetimes. As a special case of bosons, we analyze the entropy of photon gas near the horizon of the Schwarzschild black hole, which shows an area dependence similar to the Bekenstein-Hawking entropy. The results may offer new perspectives on the study of black hole thermodynamics. All these are extended to the $D+1$ dimensional spherically symmetric static spacetimes.

gr-qc↗

arXiv2021

Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity

The phase transition and thermodynamic geometry of a 4-dimensional AdS topological charged black hole in de Rham, Gabadadze and Tolley (dRGT) massive gravity have been studied. After introducing a normalized thermodynamic scalar curvature, it is speculated that its value is related to the interaction between the underlying black hole molecules if the black hole molecules exist. We show that there does exist a crucial parameter given in terms of the topology, charge, and massive parameters of the black hole, which characterizes the thermodynamic properties of the black hole. It is found that when the parameter is positive, the singlet large black hole phase does not exist for sufficient low temperature and there is a weak repulsive interaction dominating for the small black hole which is similar to the Reissner-Nordström AdS black hole; when the parameter is negative, an additional phase region describing large black holes also implies a dominant repulsive interaction. These constitute the distinguishable features of dRGT massive topological black hole from those of the Reissner-Nordström AdS black hole as well as the Van der Waals fluid system.

gr-qc↗

arXiv2021

Ruppeiner Geometry of the RN-AdS Black Hole Using Shadow Formalism

The connection between the shadow radius and the Ruppeiner geometry of a charged static spherically symmetric black hole is investigated. The normalized curvature scalar is adopted, and its close relation to the Van der Waals-like and Hawking-Page phase transition of Reissner-Nordström AdS black hole is studied. The results show that the shadow radius is a useful tool to reveal the correct information of the phase structure and the underlying microstructure of the black hole, which opens a new window to investigate the strong gravity system from the observational point of view.

gr-qc↗