Phase Transition Of Black Holes Research Articles

Topological interpretation of extremal and Davies-type phase transitions of black holes

Topological arguments are currently being used as a novel scheme to discern the properties of black holes while ignoring their detailed structure and specific field equations. Among various avenues of black hole physics, where this novel approach is being utilized, the phase transition in black hole thermodynamics lies at the forefront. There are several types of phase transition in black holes; such as the van der Waals type phase transition, Davies-type phase transition, extremal phase transition, and Hawking-Page (HP) transition. So far, the topological interpretation, where the critical point has been identified with the non-zero topological charge, has been obtained only for the van der Waals type phase transition and HP transition in different spacetimes. To complete the picture, here we provide the same interpretation for two other phase transitions: Davies-type phase transition and extremal phase transition. The entire analysis is general and is valid for any spacetime where these types of phase transitions are observed. More importantly, our analysis suggests that amid the apparent differences in these phase transitions, they share the same topological characteristics, i.e. non-zero topological charge arising from different thermodynamic potentials in different types of phase transition.

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.

Topology of Born–Infeld-AdS black hole phase transitions: Bulk and CFT sides

The thermodynamic criticality of the AdS black holes serves as an important structure during the thermal phase transition. This paper discusses about the critical points and their topology during thermal phase transitions of the Born–Infeld AdS black holes. We make such investigations using two different topological approaches, namely, using Duan’s topological current ϕ-mapping theory, and the off-shell free energy. Within Duan’s formalism, we observe that for a given value of the Born–Infeld parameter b, there exists an associated electric charge parameter Q, which is highly sensitive to the topological phase transitions. This way we examine the connections of the first-order phase transition and the topological nature of the critical points. We find that the topological nature has a possible breakdown in certain parametric ranges. In effect, we determine the unconventional and the conventional phase critical points as the creation (topologically vortex) and annihilation (topologically anti-vortex) points (pairs). As the second approach, we call the off-shell free energy to determine the topological classes: of which one corresponds to the AdS-Schwarzschild black hole phases, while the other provides a possible topological phase transition. Here we also reveal a novel phase transition between two unstable phases, namely, the unstable small black hole and the intermediate black holes. For certain parametric values of the Born–Infeld parameter and the pressure, we also study the different topological descriptions that inevitably correspond to the AdS-Reissner–Nordström black hole phases. As a consistency check of the critical points during the topological phase transitions, we study the vortex/anti-vortex annihilation thermodynamics from local as well as global thermodynamic viewpoints. At the end, a special emphasis has been put on phase transition from the conformal field theory perspective revealing that the Born–Infeld-AdS black hole and its dual CFT share identical topology. Consequently, any topological transition that occurs in the bulk corresponds to a parallel transition in the dual CFT.

Thermal analysis of gravitational decoupling black hole solution

In this work, we examine the thermodynamic properties of the hairy black holes that develop when the Reissner–Nordström geometry is applied to the gravitational decoupling method. Gibbs free energy and energy emission are also examined in our investigation. We compute several parameters to evaluate the local and global thermodynamic stability, including the Hawking temperature, geometric mass, and heat capacity. The first law of thermodynamics calculates the black hole's temperature and assesses the energy emission rate. We investigate the black hole's phase transition behavior by calculating the Gibbs free energy, paying particular attention to the swallowing tails.

Topological interpretation of black hole phase transition in Gauss–Bonnet gravity

Phase transitions of Einstein–Gauss–Bonnet black holes are studied using Duan’s [Formula: see text]-field topological current theory, where black holes are treated as topological defects in the thermodynamic parameter space. The kinetics of thermodynamic defects are studied using Duan’s bifurcation theory. In this picture, a first-order phase transition between small/large black hole phases is interpreted as the interchange of winding numbers between the defects as a result of some action at a distance. We observe a first-order phase transition between small/large black holes for [Formula: see text] Einstein–Gauss–Bonnet theory similar to Reissner–Nordström black holes in AdS space. This implies that these black hole solutions share the same topology and phase structure. We have also studied the phase transition of neutral black holes in [Formula: see text] and found a transition between unstable small and large stable black hole phases similar to the case of neutral black holes in AdS space. Recently, it has been conjectured that black holes with similar topological structure exhibit the same thermodynamic properties. Our results strengthen the conjecture by connecting the topological nature of black holes to phase transitions.

Thermodynamical analysis with extended phase transition of AdS hairy black hole in gravitational decoupling theory

This article explores various thermodynamical aspects and the extended phase space of the AdS hairy black hole within the context of gravitational decoupling. This study focused on thermodynamic properties such as geometrical mass, Hawking temperature, entropy, specific heat, Gibbs free energy (both locally and globally) and P-V criticality at the horizon radius. The thermodynamic stability of the AdS hairy black hole has been established based on its positive heat capacity. The analysis of Gibbs free energy is utilized to investigate the behavior of the first-order phase transition. Thermodynamic pressure, denoted by P, is related to the cosmological constant by the formula P=−Λ8π . In addition, a numerical investigation has been carried out to examine the equation of the state parameter and its critical values.

Triple points and phase transitions of D-dimensional dyonic AdS black holes with quasitopological electromagnetism in Einstein-Gauss-Bonnet gravity

Triple points and phase transitions of <i>D</i>-dimensional dyonic AdS black holes with quasitopological electromagnetism in Einstein-Gauss-Bonnet gravity

Phase structure of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

By considering the concept of the modified Chaplygin gas (MCG) as a single fluid model unifying dark energy and dark matter, we construct a static, spherically charged black hole (BH) solution in the framework of General Relativity. The P–V criticality of the charged anti-de Sitter (AdS) BH with a surrounding MCG is explored in the context of the extended phase space, where the negative cosmological constant operates as a thermodynamical pressure. This critical behavior shows that the small/large BH phase transition is analogous to the van der Waals liquid/gas phase transition. Accordingly, along the P–V phase spaces, we derive the BH equations of state and then numerically evaluate the corresponding critical quantities. Similarly, critical exponents are identified, along with outcomes demonstrating the scaling behavior of thermodynamic quantities near criticality to a universal class. The use of geometrothermodynamic (GT) tools finally offers a new perspective on the discovery of the critical phase transition point. At this stage, we apply a class of GT tools, such as Weinhold, Ruppeiner, HPEM, and Quevedo classes I and II. The findings are therefore non-trivial, as each GT class metric captures at least either the physical limitation point or the phase transition critical point. Overall, this paper provides a detailed study of the critical behavior of the charged AdS BH with surrounding MCG.

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.

Thermodynamics and Phase Transitions of Dyonic AdS Black Holes in Gauss-Bonnet-Scalar Gravity

In this paper, by treating the cosmological constant as a thermodynamic pressure, we study the thermodynamics and phase transitions of the dyonic AdS black holes in Gauss-Bonnet-Scalar gravity, where the conformal scalar field is considered. In a more general extended phase space, we first verified the first law of black hole thermodynamics, and find that it is always true. Meanwhile, the corresponding Smarr relation is also obtained. Then, we found that this black hole exhibits interesting critical behaviors in six dimensions, i.e., two swallowtails can be observed simultaneously. Interestingly, in a specific parameter space, we observed the small/intermediate/large black hole phase transitions, with the triple point naturally appearing. Additionally, the small/large black hole phase transition, similar to the liquid/gas phase transition of the van der Waals fluids, can also be found in other parameter regions. Moreover, we note that the novel phase structure composed of two separate coexistence curves discovered in the dyonic AdS black holes in Einstein-Born-Infeld gravity disappears in Gauss-Bonnet-Scalar gravity. This suggests that this novel phase structure may be related to gravity theory, and importantly, it is generally observed that the triple point is a universal property of dyonic AdS black holes. On the other hand, we calculated the critical exponents near the critical points and found that they share the same values as in mean field theory. Finally, it is true that these results will provide some deep insights into the interesting thermodynamic properties of the dyonic AdS black holes in the background of conformal scalar fields.

View of thermodynamic phase transition of the charged Gauss–Bonnet AdS black hole via the shadow

We examine thermodynamic phase transition (PT) of the charged Gauss–Bonnet AdS black hole (BH) by utilizing the shadow radius. In this system, we rescale the corresponding Gauss–Bonnet coefficient α by a factor of 1/(D–4), and ensure that α is positive to avoid any singularity problems. The equation derived for the shadow radius indicates that it increases as the event horizon radius increases, making it an independent variable for determining BH temperature. By investigating the PT curve in relation to shadows, we can observe that the shadow radius can be used as an alternative to the event horizon radius in explaining the phenomenon of BH PT. Furthermore, the results indicate that an increase in the parameter α corresponds to a decrease in the temperature of the BH. By utilizing the relationship between the temperature and the shadow radius, it is possible to obtain the thermal profile of the Gauss–Bonnet AdS BH. It is evident that there is an N-type variation in temperature for pressures P < P c. Additionally, as the parameter α increases, the region covered by shadow expands while the temperature decreases. The utilization of BH shadows as a probe holds immense significance in gaining a deeper understanding of BH thermodynamic behavior.

Reentrant phase transition in holographic thermodynamicsof Born–Infeld AdS black hole

In this paper, we study the phase tranisions in the extended holographic thermodynamics of Born–Infeld AdS black holes. The extended gravitational thermodynamics of black holes is related to the thermodynamics of the dual field theory by varying both cosmological constant and Newton’s constant. With topological analysis and numerical calculation, we find that the reentrant large-small-large black hole phase transition still exists in D=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=4$$\\end{document}. Interestingly, a similar reentrant phase transition is also observed in the dual field theory, between the high-, low- and high-entropy thermal states. For higher dimension D>4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D>4$$\\end{document}, only the van der Waals like phase transition is observed, both in the bulk and the dual field theory.

Dynamics and kinetics of phase transition for regular AdS black holes in general relativity coupled to nonlinear electrodynamics

We study the stochastic dynamics and kinetics of the phase transition of the regular black holes in Anti-de Sitter spacetime by employing the free energy landscape. Our investigation focuses on two important classes of regular black hole solutions, namely the Hayward and Bardeen, which can be obtained from coupling of non-linear electrodynamics. The dynamics of the phase transition is described by the Fokker–Planck equation, using which, we investigate the probabilistic evolution of regular AdS black holes. We solve this equation numerically by imposing both reflecting and absorbing boundary conditions and appropriate initial conditions. In this context, the on-shell Gibbs free energy is treated as a function of the event horizon radius, where the difference of the event horizon radii in different phases serves as the order parameter for the phase transition. The study allows us to probe the dynamic process of transitioning between coexisting small and large black hole phases due to thermal fluctuations, as quantified by the calculation of the first passage time. Furthermore, we explore the influence of temperature on this dynamic process. This research contributes to a deeper understanding of the microstructures of regular AdS black holes.

Thermodynamical phase transitions of AdS black hole in Horava–Lifshitz gravity

In this paper, we investigate the thermodynamical phase transitions of the spherically symmetric AdS black hole in Horava–Lifshitz (HL) gravity for the detailed balance violation parameter [Formula: see text]. First, by calculating the HP temperature [Formula: see text], the minimum temperature [Formula: see text] and the Gibbs free energy [Formula: see text] of the AdS black hole in different values of parameter [Formula: see text], we find that the HP phase transition can occur at all pressures. Comparing the HP temperature [Formula: see text] with the minimum temperature [Formula: see text], we notice that the ratio of [Formula: see text] tends to 1 when [Formula: see text]. Second, for the small–large black hole phase transition of the AdS black hole, we discover that the black hole heat capacity is divergent at the minimum temperature [Formula: see text], the small–large black hole phase transition occurs at the same time. Furthermore, the black hole entropy also exists [Formula: see text] when [Formula: see text], and [Formula: see text] when the black hole temperature has its minimum [Formula: see text], we surprisingly find that the ratio of [Formula: see text] tends to [Formula: see text] when the dimension [Formula: see text], which provides a general relation between the Hawking–Page phase transition and the small–large black hole phase transition of the AdS black hole in the large dimension. All in all, the ratios of typical temperature and entropy of two kinds of phase transitions tend to natural constant in the large dimension limit, which may imply to understand the nature of two different phase transitions.

Thermodynamics, Ruppeiner geometry, and topology of Born-Infeld black hole in asymptotic flat spacetime

In the extended phase space, Born-Infeld anti-de Sitter black holes exhibit diverse phase transitions including the van der Waals type and reentrant phase transitions. In this paper, we aim to investigate the potential thermodynamical features for Born-Infeld black holes when the cosmological constant vanishes. Quite differently, although there present the swallow tail behavior of the free energy and temperature-entropy criticality, no phase transition will occur when we consider the thermodynamical stability. Further, based on these findings, the phase structures are explicitly shown with the stable, unstable black hole, and non-black hole regions. After excluding the non-black hole region, we observe that the scalar curvature of the Ruppeiner geometry is always positive, indicating a dominant repulsive interaction for both the stable and unstable black holes. Particularly, we also establish the topology for the thermodynamical critical point. By calculating the topological number, we confirm that this critical point of the Born-Infeld black holes is a conventional one. Although it is not an indicator of the first small-large black hole phase transition, it does signify the emergence of stable intermediate black holes. All these results uncover the thermodynamical features of the Born-Infeld black holes in the absence of the cosmological constant.

Dynamic phase transition of black holes in massive gravity

The dynamical properties of small-large black hole phase transition in dRGT non-linear massive gravity theory are studied based on the underlying free energy landscape. The free energy landscape is constructed by specifying the Gibbs free energy to every state, and the free energy profile is used to study the different black hole phases. The small-large black hole states are characterized by probability distribution functions and the kinetics of phase transition are described by the Fokker–Planck equation. Further, a detailed study of the first passage process is presented which describes the dynamics of phase transitions. Finally, we have investigated the effect of mass and topology on the dynamical properties of phase transitions of black holes in dRGT non-linear massive gravity theory.

Physical viability of exponential entropy on charged AdS black hole through thermodynamic geometries

A detailed discussion on phase transition, stability and microscopic structure of a charged black hole in anti-de Sitter (AdS) by using exponential entropy is presented. For this black hole, the thermodynamic characteristics such as the Hawking temperature, specific heat and the P-v curve will be developed and investigated with the variation of black hole horizon radius and monopole parameter. We also study the scalar curvatures of this black hole by using several thermodynamic geometry formulations, such as the Ruppeiner, Weinhold, HPEM, Quevedo in view of exponential entropy. Moreover, we extract the HPEM and Quevedo formulations of the charged AdS black hole which may provide more data on the phase-transition than the Weinhold and Ruppeiner techniques.

4[formula omitted] AdS Einstein–Gauss–Bonnet black hole endowed with Lorentzian noncommutativity: [formula omitted] criticality, Joule–Thomson expansion, and shadow

In this article, we get a static, spherically symmetric 4D-AdS EGB black hole inspired by noncommutative geometry, where noncommutativity is expressed by a Lorentzian distribution. The noncommutativity correction has changed the relevant thermodynamic quantities. The cosmological constant Λ is interpreted as a dynamical pressure, and the noncommutative parameter Θ is treated as a thermodynamic variable to keep the first thermodynamic law and the Smarr formula in place. Our solution’s P−v criticality was investigated in the extended phase space, where the large/small black hole phase transition arises for the noncommutative 4D-AdS EGB black hole. That is, the noncommutativity parameter influences the phase transition as well as the critical pressure, horizon radius, and temperature; as a result, the critical ratio is also influenced and does not yet remain universal, as in the Van der Waals systems. The Joule–Thomson expansion has been studied in extended phase space. We acquired the inversion points (Pi,Ti) as a function of Θ, which allowed us to analyze the isenthalpic and inversion curves in the T−P plane and demonstrate the cooling and heating zones. In addition, it has been shown that the shadow radius is reduced when we increase the noncommutativity parameter, as is the peak of the associated energy emission rate, which decreases with the rise of the parameter Θ.

Continuous phase transition of the de Sitter spacetime with charged black holes and cloud of strings and quintessence* *Supported by the Natural Science Foundation of China (11705106, 12075143), the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province (2020L0471, 2020L0472), the Science Technology Plan Project of Datong City, China (2020153), the Science Foundation of Shanxi Datong University (2022Q1,

Recently, some meaningful results have been obtained by studying the phase transition, critical exponents, and other thermodynamical properties of different black holes. Especially for the Anti-de Sitter (AdS) black holes, their thermodynamical properties nearby the critical point have attracted considerable attention. However, there exists little work on the thermodynamic properties of the de Sitter (dS) spacetime with black holes. In this paper, based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law, we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence (i.e., C-dSSQ spacetime). The boundaries of the two-phase coexistence region in both and diagrams are obtained. The coexistent curve and the latent heat of phase transition for this system are also investigated. Furthermore, we analyze the effect of parameters (the state parameter ω and the ratio of two horizon radii /) on the two-phase coexistence region boundary. The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid (vdw) system, which is determined by the electrical potential at the horizon. These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.

Thermodynamics and microstructures of Euler–Heisenberg black hole in a cavity

Euler–Heisenberg black holes with quantum electrodynamics (QED) correction are embraced by a cavity in this paper, which serves as a boundary of the black hole spacetime and contributes to the equilibrium of the system. We explore the thermodynamic properties of the black hole, including the phase transitions and phase structures. The small/large black hole phase transition occurs for a negative QED parameter, while the reentrant phase transition can be observed for a small positive QED parameter. Then the thermodynamic geometry is investigated to diagnose microscopic interactions of black hole thermodynamic systems. For the reentrant phase transition, the small black holes are dominated by repulsion for the first-order coexistence curve, while the interaction between the small black hole molecules could be attractive or repulsive for the small/large black hole phase transition.