Phase Transition Of Black Holes Research Articles

On Rényi universality formula of charged flat black holes from Hawking-Page phase transition

Probing the thermodynamic properties of the Hawking-Page phase transition of asymptotically-flat black holes in Rényi statistics. We reveal the evidence for the persisting of the dual universal formula associated with the Hawking-Page (HP) and minimum black hole thermodynamical transition points. Our study unveils the universal properties of the black holes in different statistics, in particular beyond the Gibbs-Boltzmann formalism, and motivates a further promising bridge between the nonextensivity Rényi parameter λ and the cosmological constant Λ. Besides, we discover that universal ratios related to horizon radius, Rényi temperature, and entropy can be shown to appear in presence of such a transition.

The extended uncertainty principle effects on the phase transitions of Reissner-Nordström and Schwarzschild black holes

In this paper, we investigate the phase transitions of Reissner-Nordström (RN) and Schwarzschild black holes for the extended uncertainty principle (EUP) framework. Considering temperature T, charge Q and electric potential Φ as the state parameters, we show the van der Waals (vdW) like phase transition of RN black hole in Q−Φ diagrams and find the critical points depending on EUP parameter α. Furthermore, we find Hawking-Page like phase transition for Schwarzschild black hole. The results imply that the black holes in asymptotically flat space have the similar phase structure with the black holes in anti-de Sitter (AdS) space.

AdS Black Holes in the Framework of Nonlinear Electrodynamics, Thermodynamics, and Joule–Thomson Expansion

The thermodynamics and phase transitions of magnetic Anti-de Sitter black holes were studied. We considered extended-phase-space thermodynamics, with the cosmological constant being a thermodynamic pressure and the black hole mass being treated as a chemical enthalpy. The extended-phase-space thermodynamics of black holes mimic the behavior of a Van der Waals liquid. Quantities conjugated to the coupling of nonlinear electrodynamics (NED) and a magnetic charge are obtained. Thermodynamic critical points of phase transitions are investigated. It was demonstrated that the first law of black hole thermodynamics and the generalized Smarr relation hold. The Joule–Thomson adiabatic expansion of NED-AdS black holes is studied. The dependence of inversion temperature on pressure and the minimum of the inversion temperature are found.

Quantum corrections to the thermodynamics and phase transition of a black hole surrounded by a cavity in the extended phase space

In the extended phase space, we investigate the rainbow gravity-corrected thermodynamic phenomena and phase structure of the Schwarzschild black hole surrounded by a spherical cavity. The results show that rainbow gravity has a very significant effect on the thermodynamic phenomena and phase structure of the black hole. It prevents the black hole from total evaporation and leads to a remnant with a limited temperature but no mass. Additionally, we restore the P − V criticality and obtain the critical quantities of the canonical ensemble. When the temperature or pressure is smaller than the critical quantities, the system undergoes two Hawking-Page-like phase transitions and one first-order phase transition, which never occurs in the original case. Remarkably, our findings demonstrate that the thermodynamic behavior and phase transition of the rainbow SC black hole surrounded by a cavity in the extended phase space are analogous to those of the Reissner–Nordström anti-de Sitter black hole. Therefore, rainbow gravity activates the effect of electric charge and cutoff factor in the evolution of the black hole.

Thermodynamics and phase transition of BTZ black hole in a cavity

In this paper, we study the thermodynamics and phase transition of a BTZ black hole in a finite space region, namely a cavity. By imposing a temperature-fixed boundary condition on the wall of the cavity and evaluating the Euclidean action, we derive the thermodynamic quantities and then construct the first law of thermodynamics for a static and neutral BTZ black hole, a rotating BTZ black hole and a charged BTZ black hole, respectively. We prove that heat capacities of these three types of black holes are always non-negative. Considering a grand canonical ensemble, we find that the non-extreme rotating black hole and the charged black hole are locally thermodynamically stable by calculating the Hessian matrix of their internal energy. At the phase transition level, it shows that for the static and neutral BTZ black hole, the phase transition only exists between thermal AdS3 spacetime and the black hole. The temperature where the phase transition occurs is only determined by the cavity radius. For rotating and charged cases, there may exist an extra second-order phase transition between the black hole and the black hole-cavity merger state. The phase structure of a BTZ black hole in a cavity shows strong dissimilarities from that without the cavity.

QCD phase diagram by holography

We explore the QCD phase diagram by constructing a holographic QCD model using the Einstein-Maxwell-Scalar system. The chiral transition is investigated by adding a probe scalar and the confinement transition is studied by adding a probe string into the system. By interpreting the black hole phase transition in the bulk spacetime as the quarkyonic transition in the dual QCD theory and introducing the bypass mechanism for the deconfinement transition, we give an explanation why chiral symmetry breaking and deconfinement transition lines coincide with each other despite their different physical origins.

Phase equilibrium and microstructure of topological AdS black holes in massive gravity * *Supported in part by the National Natural Science Foundation of China (11705106, 11705107, 12075143), Science and Technology Innovation Project of Shanxi Higher Education (2016173) and the Doctoral Sustentation Fund of Shanxi Datong University

In order to clearly understand the gravitational theory through the thermal properties of the black hole, it is important to further investigate the first-order phase transition of black holes. In this paper, we adopt different conjugate variables ( , , , and ) and apply Maxwell's equal-area law to study the phase equilibrium of a topological black hole in massive gravity. The condition and latent heat of phase transition are displayed as well as the coexistent curve of . The result shows that the phase transition of this system is the high/low electric potentials one, not only the large/small black holes one. We also analyze the effect of the model's parameters on phase transition. Furthermore we introduce a new order parameter to probe the microstructure of this system. This work will provide the theoretical basis to study the phase structure of topological black holes in massive gravity and to further explore the gravitational theory.

Impacts of Generalized Uncertainty Principle on the Black Hole Thermodynamics and Phase Transition in a Cavity

In this work, we conduct a study regarding the thermodynamic evolution and the phase transition of a black hole in a finite spherical cavity subject to the generalized uncertainty principle. The results demonstrate that both the positive and negative generalized uncertainty principle parameters β0 can significantly affect the thermodynamic quantities, stability, critical behavior, and phase transition of the black hole. For β0 > 0, the black hole forms a remnant with finite temperature, finite mass, and zero local heat capacity in the last stages of evolution, which can be regarded as an elementary particle. Meanwhile, it undergoes one second-order phase transition and two Hawking-Page-type phase transitions. The Gross-Perry-Yaffe phase transition occurs for both large black hole configuration and small black hole configuration. For β0 < 0, the Gross-Perry-Yaffe phase transition occurs only for large black hole configuration, and the temperature and heat capacity of the black hole remnant is finite, whereas its mass is zero. This indicates the remnant is metastable and would be in the Hawking-Page-type phase transition forever. Specifically, according to the viewpoint of corpuscular gravity, the remnant can be interpreted as an additional metastable tiny black hole configuration, which never appears in the original case and the positive correction case.

Triple points and novel phase transitions of dyonic AdS black holes with quasitopological electromagnetism

Quasitopological electromagnetism has an important influence on the strong gravity of dyonic black holes. For example, three photon spheres, with one being stable, are found, and we wish to test them with the observed black hole shadow. We are primarily concerned with the thermodynamics and phase transition for a dyonic anti--de Sitter (AdS) black hole when quasitopological electromagnetism is included. Unlike in a black hole solution without quasitopological electromagnetism, we observe a triple point phase structure by varying the coupling parameters. Of particular interest, for certain parameter values, two separate coexistence curves are present, which is an additional novel phase structure that is absent in a black hole solution without quasitopological electromagnetism. The critical exponents share the same values as mean field theory. These results uncover the intriguing properties of dyonic AdS black holes with quasitopological electromagnetism from a thermodynamic point of view.

Kinetics of Hawking-Page phase transition with the non-Markovian effects

Based on the free energy landscape description of Hawking-Page phase transition, the transition process from the Schwarzschild-anti-de Sitter black hole to the thermal anti-de Sitter space are considered to be stochastic under the thermal fluctuations. If the correlation time of the effective thermal bath is comparable or even longer than the oscillating time of the spacetime state in the potential well on the free energy landscape, the non-Markovian model of the black hole phase transition is required to study the kinetics of the transition processes. The non-Markovian or memory effect is represented by the time dependent friction kernel and the kinetics is then governed by the generalized Langevin equation complemented by the free energy potential. As the concrete examples, we study the effects of the exponentially decay friction kernel and the oscillatory friction kernel on the kinetics of Hawking-Page phase transition. For the exponentially decayed friction, the non-Markovian effects promote the transition process, and for the oscillatory friction, increasing the oscillating frequency also speeds up the transition process.

Topological black holes with curvature induced scalarization in the extended scalar-tensor theories

We study the perturbative behaviour of topological black holes in the presence of a cosmological constant and a scalar field coupled to the Gauss-Bonnet term. We calculate both analytically and numerically the quasi-normal modes of scalar perturbations in the extended scalar-tensor-Gauss-Bonnet gravity. In the case of small black holes we find a phase transition of the topological black hole to a hairy configuration.

Path integral and instantons for the dynamical process and phase transition rate of Reissner-Nordström-AdS black holes

We propose a new approach to study the dynamical phase transition of RNAdS black holes on the underlying free energy landscape. By formulating a path integral framework, we can quantify the kinetic paths representing the history from the initial state to the end state, which provides us a visualized yet quantified picture about how the phase transition proceeds. Based on these paths, we derive the analytical formulas for the time evolution of the transition probability and provide a physical interpretation of the contribution to the probability from one "pseudomolecule" ("anti-pseudomolecule"), which is actually the phase transition rate from the small(large) to the large(small) black hole state. These numerical results show a good consistency with the underlying free energy landscape topography.

Notes on complexity growth rate, grand potential and partition function

We examine the complexity/volume conjecture and further investigate the possible connections between complexity and partition function. The complexity/volume 2.0 states that the complexity growth rate $\mathcal{\dot{C}}\sim PV$. In the standard statistics, there is a fundamental relation among $PV$, the grand potential $\Omega$ and the partition function $\mathcal{Z}$. By using this relation, we are able to construct an ansatz between complexity and partition function. The complexity/partition function relation is then utilized to study the complexity of the thermofield double state of extended SYK models for various conditions. The relation between complexity growth rate and black hole phase transition is also discussed.

Some remarks on criticality and thermodynamics of the dynamic phantom AdS black holes

In this paper, we discuss the thermodynamic phase-transition, thermal stability and criticality of dynamic phantom AdS black hole (BH) in the presence of electric charge e and magnetic charge g. To accomplish this, we construct the specific heat and other important thermodynamical parameters which help us to investigate the stability and criticality. The thermodynamical properties of dynamic phantom AdS BH are examined by utilizing the specific heat (C_P), volume expansivity (beta ), isothermal compressibility (kappa ), Temperature vs Entropy (T–S), Pressure vs Volume (P–V) and Gibbs free energy G, graphically. Specific heat against entropy describes the divergency behaviour, which produces the second-order phase transition. We also obtain isenthalpic curves for both systems in the T–P plane and determine the cooling and heating regions by utilizing Joule–Thomson expansion. Moreover, we discuss the behaviour of (P–V) isotherm that is equal to the liquid/gas transition of the Van-Der Waals fluid is exactly matched to 3/8 also known as a universal number. Furthermore, we investigate Swallow-tail behaviour and also discuss the stability and instability of the small black hole (SBH), Intermediate black hole (IBH) and large black hole (LBH).

Kinetics of a phase transition for a Kerr-AdS black hole on the free-energy landscape

By treating the order parameter as a stochastic thermal fluctuating variable for small-large black hole phase transition, we investigate the kinetic process of phase transition for the Kerr-AdS (anti--de Sitter) black holes on free energy landscape. We find that the extremal points of the off shell Gibbs free energy correspond to physical black holes. For small-large black hole phase transition, the off shell Gibbs free energy exhibits a double well behavior with the same depth. Contrary to previous research for the kinetics of phase transition for the Kerr-Newman-AdS family black holes on a free energy landscape, we find that there is a lower bound for the order parameter and the lower bound corresponds to extremal black holes. In particular, the off shell Gibbs free energy is zero instead of divergent as previous work suggested for vanishing black hole horizon radius, which corresponds to the Gibbs free energy of a thermal AdS space. The investigation for the evolution of the probability distribution for the phase transition indicates that the initial stable small (large) black hole tends to switch to stable large (small) black hole. Increasing the temperature along the coexistence curve, the switching process becomes faster and the probability distribution reaches the final stationary Boltzmann distribution at a shorter time. The distribution of the first passage time indicates the time scale of the small-large black hole phase transition, and the peak of the distribution becomes sharper and shifts to the left with the increase of temperature along the coexistence curve. This suggests that a considerable first passage process occurs at a shorter time for higher temperature. The investigation of the kinetics of phase transition might provide us new insight into the underlying microscopic interactions.

Thermodynamics of 4D dS/AdS Gauss–Bonnet black holes according to consistent gravity theory in the presence of a cloud of strings

By looking at the Lovelock theorem one can infer that the gravity model given by [1] cannot be applicable for all types of 4D Einstein–Gauss–Bonnet (EGB) curved space-time. The reason for this is that in 4D space-time, the Gauss–Bonnet invariant is a total derivative and hence it does not contribute to gravitational dynamics. Hence, the authors of [2] presented an alternative consistent EGB gravity model instead of [1] by applying a break-of-diffeomorphism property. In this work, we use the alternative model to produce a de Sitter (dS)/Anti-de Sitter (AdS) black hole metric and then investigate its thermodynamic behavior in the presence of a cloud of Nambu–Goto strings. Mathematical derivations show that the resulting diagrams of pressure vs specific volume at a constant temperature are similar to that for a van der Waals gas/fluid in an ordinary thermodynamic system in the dS sector but not in the AdS background. From this, we infer that the black hole participates in the small-to-large black hole phase transition in the dS background, while it exhibits a Hawking–Page phase transition in the AdS background. In the latter case, an evaporating black hole eventually reaches an AdS vacuum space because of its instability.

Dynamic property of phase transition for non-linear charged anti-de Sitter black holes * *Supported by the National Natural Science Foundation of China (11705106, 11475107, 12075143), the Natural Science Foundation of Shanxi Province, China (201901D111315), the Natural Science Foundation for Young Scientists of Shanxi Province, China (201901D211441), the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province (2020L0471, 2020L0472,

Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity. In this work, we investigate the phase transition and its dynamics for the charged EPYM AdS black hole. Through reconstructing Maxwell's equal-area law, we find there exists a high-/low-potential black hole (HPBH/LPBL) phase transition, not only the pure large/small black hole phase transition. The Gibbs free energy landscape ( ) is treated as a function of the black hole horizon, which is the order parameter of the phase transition due to thermal fluctuation. From the viewpoint of , the stable HPBH/LPBL states correspond to two wells of , which have the same depth. The unstable intermediate-potential black hole state corresponds to the local maximum of . Then we focus on the probability evolution governed by the Fokker–Planck equation. Through solving the Fokker–Planck equation with different reflection/absorption boundary conditions and initial conditions, the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time. Furthermore, the effect of temperature on the dynamic properties of the phase transition is also investigated.

Thermodynamic stability and P\u2013V criticality of nonsingular-AdS black holes endowed with clouds of strings

We investigate the extended phase space thermodynamics of nonsingular-AdS black holes minimally coupled to clouds of strings in which we consider the cosmological constant (Lambda ) as the pressure (P) of the black holes and its conjugate variable thermodynamical volume (V) of the black holes. Owing to the background clouds of strings parameter (a), we analyse the Hawking temperature, entropy and specific heat on horizon radius for fixed-parameter k. We find that the strings clouds background does not alter small/large black hole (SBH/LBH) phase transition but occurs at a larger horizon radius, and two second-order phase transitions occur at a smaller horizon radius. Indeed, the G–T plots exhibit a swallowtail below the critical pressure, implying that the first-order phase transition is analogous to the liquid–gas phase transition at a lower temperature and lower critical pressure. To further examine the analogy between nonsingular-AdS black holes and a liquid–gas system, we derive the exact critical points and probe the effects of a cloud of strings on P-V criticality to find that the isotherms undergo liquid–gas like phase transition for {tilde{T}},<,{tilde{T}}_c at lower {tilde{T}}_c. We have also calculated the critical exponents identical with Van der Walls fluid, i.e., same as those obtained before for arbitrary other AdS black holes, which implies that the background clouds of strings do not change the critical exponents.

Energy and entropy compensation, phase transition and kinetics of four dimensional charged Gauss-Bonnet Anti-de Sitter black holes on the underlying free energy landscape

By treating black hole as a state in canonical ensemble or in grand canonical ensemble, we study the phase transition and the kinetics of the four dimensional charged Anti-de Sitter (AdS) black hole in Gauss-Bonnet (GB) gravity based on the free energy landscape. Below the critical temperature, the free energy landscape topography has the shape of double basins with each representing one stable/unstable black hole phase (the small or the large black hole). The thermodynamic small/large black hole phase transition is determined by the equal depths of the basins. We also demonstrate the underlying kinetics of the phase transition by studying the time evolution of the probability distribution of the state in the ensemble as well as the mean first passage time (MFPT) and the kinetic fluctuations of the state switching process caused by the thermal fluctuations. The results show that the final distribution is determined by the Boltzmann law and the MFPT and its fluctuation are closely related to the free energy landscape topography through the barrier heights between the small and the large black hole states and the ensemble temperature. Furthermore, we provide a complete description of the kinetics of phase transition by investigating the temperature dependence of the MFPT and the kinetic fluctuations with different physical parameters. It is shown that the free energy is the result of the delicate balance and competition between the two relatively large numbers, the energy and entropy multiplied by temperature compared to kT. Low energy (mass) and low entropy can give rise to a stable thermodynamic state in terms of free energy minimum (energy/mass preferred) while the high energy (mass) and high entropy (entropy preferred) can also give rise to a stable state in terms of free energy minimum. The comparable free energy barrier with respect to kT makes it possible for the switching from small size black hole state to the large size black hole state under thermal fluctuations and vice versa. When the GB coupling coupling constant increases, or the electric charge (potential) increases, or the pressure (absolute value of cosmological constant) decreases, it is easier for the small black hole state to escape to the large black hole state. Meanwhile, the inverse process becomes harder, i.e. the small (large) black hole state becomes less (more) stable.

Thermodynamic geometries analysis of charged black holes with barrow entropy

We study the phase transition and thermodynamic geometries of a charged AdS black hole with a global monopole. For this purpose, we develop the thermodynamic quantities such as Hawking temperature, specific heat and pressure on horizon radius in the presence of Barrow entropy. The stability of this black hole is being observed through specific heat. Also, we investigate the thermodynamic curvatures behavior of black hole by applying Weinhold and Ruppeiner formulations. It is found that thermodynamic curvatures exhibit the attractive and repulsive nature of black hole for specific constants. We also study the thermodynamic curvature of charged BTZ black hole by fixing phase space of entropy, pressure and volume on curvature, i.e., entropy-pressure corrected curvature (RSP) and entropy-volume corrected curvature (RSV). It is found that there present a repulsive force by the charged BTZ black hole for its molecules, qualitatively or phenomenologically. However, RSV shows negative behavior initially which exhibits the attractive nature of charged BTZ black hole.