Van Der Waals-like Phase Transition Research Articles

Thermal analysis of black hole in de Rham–Gabadadze–Tolley massive gravity in barrow entropy framework

This study examines a recently hypothesized black hole solution in de Rham–Gabadadze–Tolley massive gravity. Firstly, we consider the negative cosmological constant as a thermodynamic pressure. We extract the thermodynamical properties such as Hawking temperature, heat capacity and Gibbs free energy using the barrow entropy. We also obtain a new pressure associated to the perfect fluid dark matter and discuss the first-order van der Waals-like phase transition. This black hole’s stability is investigated through specific heat and Gibbs free energy. Also, we analyze the thermodynamic curvatures behavior of black hole through geometry methods (Weinhold, Ruppeiner, Hendi-Panahiyah-Eslam-Momennia (HPEM), and geometrothermodynamics (GTD)).

P − v criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics

Boltzmann entropy-based thermodynamics of charged anti-de Sitter (AdS) black holes has been shown to exhibit physically interesting features, such as P − V criticalities and van der Waals-like phase transitions. In this work we extend the study of these critical phenomena to Kaniadakis theory, which is a non-extensive generalization of the classical statistical mechanics incorporating relativity. By applying the typical framework of condensed-matter physics, we analyze the impact of Kaniadakis entropy onto the equation of state, the Gibbs free energy and the critical exponents of AdS black holes in the extended phase space. Additionally, we investigate the underlying micro-structure of black holes in Ruppeiner geometry, which reveals appreciable deviations of the nature of the particle interactions from the standard behavior. Our analysis opens up new perspectives on the understanding of black hole thermodynamics in a relativistic statistical framework, highlighting the role of non-extensive corrections in the AdS black holes/van der Waals fluids dual picture.

Rotating Lifshitz-like black holes in F(R) gravity

Abstract One of the alternative theories of gravitation with a possible UV completion of general relativity is Horava–Lifshitz gravity. Regarding a particular class of pure F(R) gravity in three dimensions, we obtain an analytical rotating Lifshitz-like black hole solution. We first investigate some geometrical properties of the obtained solution that reduces to a charged rotating Banados–Teitelboim–Zanelli black hole in a special limit. Then, we study the optical features of such a black hole, like the photon orbit and the energy emission rate, and discuss how electric charge, angular momentum, and exponents affect them. To have acceptable optical behavior, we should apply some constraints on the exponents. We continue our investigation by studying the thermodynamic behavior of solutions in the extended phase space and explore the validity of the first law of thermodynamics as well as local thermal stability using heat capacity. Evaluating the existence of van der Waals-like phase transition, we obtain critical quantities and show how they change under the variation of black hole parameters. Finally, we construct a holographic heat engine of such a black hole and obtain its efficiency in a cycle. Comparing the obtained results with the well-know Carnot heat engine efficiency, we examine the second law of thermodynamics.

On heat properties of charged AdS black holes in Gauss-Bonnet gravity coupled with nonlinear electrodynamics

We investigate the heat properties of charged AdS black holes in the Gauss-Bonnet gravity coupled with nonlinear electrodynamics. We consider the thermodynamics of black holes from the perspective of heat capacity and show that the nonlinear electrodynamics can be helpful to improve the thermodynamic stability of black holes. We perform a two-dimensional description in order to reproduce the Hawking temperature, which confirms that the Hawking temperature has an intrinsic topological nature and holds for a higher dimensional spherically symmetric spacetime. We also analyze the Maxwell equal area law and coexistence curve, and find the existence of van der Waals-like phase transitions based on critical exponents. Moreover, we deal with a charged AdS black hole in the Gauss-Bonnet gravity coupled with nonlinear electrodynamics as a working material to study holographic heat engines and obtain an exact expression for the efficiency of a rectangular engine cycle. We then discuss the effects of nonlinear electrodynamics and Gauss-Bonnet couplings on the rectangular engine cycle and compare the efficiency of this cycle with that of the Carnot cycle.

Thermodynamics and phase transition of d-dimensional charged AdS black hole in rainbow gravity

In this paper, we have studied the thermodynamic properties of charged AdS black hole with different dimensions under rainbow gravity. At first, by employing the Heisenberg uncertainty principle and the modified dispersion relation and analyzing the effect of rainbow gravity parameter [Formula: see text] and AdS radius [Formula: see text] on the thermodynamics and phase transformation, we have found that the phase structure is related to the AdS radius [Formula: see text] and the heat capacity behaviors are quite similar for different rainbow gravity parameters [Formula: see text] and different dimensions [Formula: see text]. Then, for the rainbow gravity, introducing the analogy between the charged AdS black hole and liquid–gas systems and analyzing the critical behavior of the state equation for charged AdS black hole in different dimensions, the charged AdS black hole has Van der Waals-like phase transitions. At last, we have discussed the relationship between Gibbs free energy [Formula: see text] and Hawking temperature [Formula: see text] in different dimensions and found the typical dovetail behavior, which can be interpreted as a first-order phase transition for the charged AdS black hole under rainbow gravity.

Thermodynamic phase transitions and compressibility of rotating Bardeen(–AdS) black holes with quintessence

We derive thermodynamic quantities such as the Hawking temperature, mass, entropy, heat capacity and study the thermodynamic phase transitions of rotating Bardeen black holes surrounded by quintessence-like matter. Interpreting the cosmological parameter as thermodynamic pressure and its conjugate variable as volume, the first law of black hole thermodynamics has been modified in the Anti-de Sitter (AdS) space. It then has been used to investigate the thermodynamics of the rotating Bardeen–AdS black hole with quintessence matter. Properties of the thermodynamic volume have also been analyzed through the study of compressibility and sound speed of the black hole. The black hole sound speed is associated with the adiabatic compressibility, and it equals the light speed for nonrotating black holes and decreases with increasing angular momentum. The nonrotating black holes are adiabatically incompressible, and as the angular momentum attains a maximum value in the extremal case, the compressibility grows maximum. We further derive the equation of state in the extended phase space and explore the critical behaviors of the black hole in the canonical ensemble. Graphs of phase transitions and critical behaviors show an accentuated influence of quintessence matter on the thermodynamic phase transitions and stability of the black holes and support the van der Waals-like phase transition behavior.

Asymptotic critical behavior of holographic superconductor phase transition — the spectrum of excited states becomes continuous at T = 0

Within the framework of AdS/CFT duality, excited states of the conformal field living at the global AdS boundary of a four-dimensional spacetime Einstein gravity are investigated analytically in the probe limit where the field equations are linearized. At asymptotically large values, the threshold chemical potential for the appearance of excited condensate states are discrete, equal spacing, with the gap approaches zero logarithmically in the limit T → 0. Remarkably, numerical results show that, this behavior applies even for states as low as for the first or the second excited state of the condensate. This is especially significant on the liquid side of the black hole van der Waals-like phase transition (small or zero topological charge) where there seems to be no gap between the ground state and the first excited state at zero temperature. We postulate that, at the exact limit T = 0 where the gap is zero, the spectrum of threshold chemical potentials becomes continuous, all excited states of the condensate are activated above a finite chemical potential, suggesting a new quantum phase transition as a function of the chemical potential. Previous studies have largely missed this continuous spectrum of excited states in the T → 0 limit. This fact should be taken into account carefully in AdS/CFT duality studies.

Note on stability and holographic subregion complexity

We study holographic subregion complexity in a spatially anisotropic field theory, which expresses a confinement-deconfinement phase transition. Its holographic dual is a five-dimensional anisotropic holographic model characterized by a Van der Waals-like phase transition between small and large black holes. We propose a new interpretation from the informational perspective to determine the stable and unstable thermodynamically solutions. According to this proposal, the states which need (more) less information to be specified characterize the (un) stable solutions. We similarly offer an interpretation to determine the stable and unstable solutions based on the resource of a computational machine, such that the solutions are (un) stable if computational resource (decreases) increases with the increase of temperature. We observe that the effect of anisotropy on holographic subregion complexity is decreasing. This decreasing effect can be interpreted by considering a whole closed system consisting of the state and its environment in which the complexity of the mixed state decreases and complexity of the environment increases.

Holographic anisotropic model for light quarks with confinement-deconfinement phase transition

We present a five-dimensional anisotropic holographic model for light quarks supported by Einstein-dilaton-two-Maxwell action. This model generalizing isotropic holographic model with light quarks is characterized by a Van der Waals-like phase transition between small and large black holes. We compare the location of the phase transition for Wilson loops with the positions of the phase transition related to the background instability and describe the QCD phase diagram in the thermodynamic plane — temperature T and chemical potential μ. The Cornell potential behavior in this anisotropic model is also studied. The asymptotics of the Cornell potential at large distances strongly depend on the parameter of anisotropy and orientation. There is also a nontrivial dependence of the Cornell potential on the boundary conditions of the dilaton field and parameter of anisotropy. With the help of the boundary conditions for the dilaton field one fits the results of the lattice calculations for the string tension as a function of temperature in isotropic case and then generalize to the anisotropic one.

Phase transition and quasinormal modes for charged black holes in 4D Einstein-Gauss-Bonnet gravity * *Supported by the National Natural Science Foundation of China (11605152, 11675139, 51802247) and Outstanding youth teacher programme from Yangzhou University

In four-dimensional Einstein-Gauss-Bonnet (EGB) gravity, we consider the thermodynamic and phase transitions of (charged) AdS black holes. For the negative GB coefficient , the system allows two physical critical points, corresponding to the reentrant phase transition, when the charge . For arbitrary , the system always leads to a van der Waals phase transition. We then study the quasinormal modes (QNMs) of massless scalar perturbations to probe the van der Waals-like phase transition between small and large black holes (SBH/LBH) for (charged) AdS black holes. We find that the signature of this SBH/LBH phase transition in the isobaric process can be detected since the slopes of the QNM frequencies change dramatically in small and large black holes near the critical point. The obtained results further support that QNMs can be a dynamic probe of thermodynamic properties in black holes.

Ruppeiner geometry, reentrant phase transition, and microstructure of Born-Infeld AdS black hole

Born-Infeld AdS black hole exhibits a reentrant phase transition for certain values of the Born-Infeld parameter $b$. This behaviour is an additional feature compared to the van der Waals like phase transition observed in charged AdS black holes. Therefore, it is worth observing the underlying microscopic origin of this reentrant phase transition. Depending on the value of the parameter $b$, the black hole system has four different cases: no phase transition, a reentrant phase transition with two scenarios, or a van der Waals-like (standard) phase transition. In this article, by employing a novel Ruppeiner geometry method in the parameter space of temperature and volume, we investigate the microstructure of Born-Infeld AdS black hole via the phase transition study, which includes standard and reentrant phase transition. We find that the microstructures of the black hole that lead to standard and reentrant phase transitions are distinct in nature. The standard phase transition is characterised by the typical RN-AdS microstructure. In this case, the small black hole phase has a dominant repulsive interaction for the low temperature case. Interestingly, during the reentrant phase transition, displayed by the system in a range of pressures for specific $b$ values, the dominant attractive nature of interaction in the microstructure is preserved. Our results suggest that in the reentrant phase transition case, the intermediate black holes behave like a bosonic gas, and in the standard phase transition case the small black holes behave like a quantum anyon gas. In both cases, the large black hole phase displays an interaction similar to the bosonic gas. The critical phenomenon is observed from the curvature scalar, including the signature of the reentrant phase transition.

Thermal image and phase transitions of charged AdS black holes using shadow analysis

We investigate the relations between the black hole shadow and charged AdS black hole critical behavior in the extended phase space. Using the thermo-shadow formalism built in Ref. 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 the observational point of view.

GUP effect on thermodynamical properties of the noncommutative rotating BTZ black hole

In this paper, we investigated the quantum gravity effects on the thermal properties of the [Formula: see text]-dimensional noncommutative rotating Banados–Teitelboim–Zanelli (NCR-BTZ) black hole in the context of quantum tunneling of relativistic particles. These include Hawking temperature, the thermally local and global stability conditions, and the phase transitions. For this purpose, in the framework of the generalized uncertainty principle (GUP), we used the Hamilton–Jacobi approach to calculate the tunneling probability for a massive scalar, Dirac, and vector boson particles from the [Formula: see text]-dimensional NCR-BTZ black hole. We found that the modified Hawking temperature of the black hole depends on the black hole properties, on the tunneling particle properties, on the noncommutative parameter, and on the GUP parameter. Using the modified Hawking temperature, we calculated the modified heat capacity, and then we discussed the local thermodynamic stability conditions for the black hole. The black hole may undergo a first-type phase transition to become stable under the scalar particle tunneling whereas, it might undergoes both the first and the second-type phase transitions under the both Dirac and vector boson particles tunneling process. Furthermore, we calculated the Gibbs free energy of the black hole, and we investigated the global stability conditions. We observed that Hawking–Page phase transition may occur in the presence of the quantum gravity effect under the tunneling process of scalar, Dirac, and vector boson particles. In the context of quantum gravity effect, we also derived the modified equation of state to investigate the critical behavior of the commutative rotating BTZ black hole. Finally, we shown that Van der Waals-like phase transition may occur in the context of tunneling process of both Dirac and vector boson particle, whereas it may not occur for the tunneling of scalar particle.

Holographic entanglement entropy in anisotropic background with confinement-deconfinement phase transition

We discuss a general five-dimensional completely anisotropic holographic model with three different spatial scale factors, characterized by a Van der Waals-like phase transition between small and large black holes. A peculiar feature of the model is the relation between anisotropy of the background and anisotropy of the colliding heavy ions geometry. We calculate the holographic entanglement entropy (HEE) of the slab-shaped region, the orientation of which relatively to the beams line and the impact parameter is characterized by the Euler angles. We study the dependences of the HEE and its density on the thermodynamic (temperature, chemical potential) and geometric (parameters of anisotropy, thickness, and orientation of entangled regions) parameters. As a particular case the model with two equal transversal scaling factors is considered. This model is supported by the dilaton and two Maxwell fields. In this case we discuss the HEE and its density in detail: interesting features of this model are jumps of the entanglement entropy and its density near the line of the small/large black hole phase transition. These jumps depend on the anisotropy parameter, chemical potential, and orientation. We also discuss different definitions and behavior of c-functions in this model. The c-function calculated in the Einstein frame decreases while ℓ is increasing for all ℓ in the isotropic case (in regions of (μ, T )-plane far away from the line of the phase transition). We find the non-monotonicity of the c-functions for several anisotropic configurations, which however does not contradict with any of the existing c-theorems since they all are based on Lorentz invariance.

Thermodynamics and phase transition of a Gauss-Bonnet black hole in a cavity

Considering a canonical ensemble, in which the temperature and the charge on a wall of the cavity are fixed, we investigate the thermodynamics of a D-dimensional Gauss-Bonnet black hole in a finite spherical cavity. Moreover, it shows that the first law of thermodynamics is still satisfied. We then discuss the phase structure and transition in both five and six dimensions. Specifically, we show that there always exist two regions in the parameter space. In one region, the system possesses one single phase. However in the other region, there could coexist three phases and a van der Waals-like phase transition occurs. Finally, we find that there is a fairly close resemblance in thermodynamic properties and phase structure of a Gauss-Bonnet-Maxwell black hole, either in a cavity or in anti-de Sitter space.

Probing correlation between photon orbits and phase structure of charged AdS black hole in massive gravity background

The phase structure of charged anti-de Sitter black hole in massive gravity is investigated using the unstable circular photon orbits formalism, concretely we establish a direct link between the null geodesics and the critical behavior thermodynamic of such black hole solution. Our analysis reveals that the radius and the impact parameter corresponding to the unstable circular orbits can be used to probe the thermodynamic phase structure. We also show that the latter are key quantities to characterize the order of Van der Waals-like phase transition. Namely, we found a critical exponent around [Formula: see text]. All these results support further that the photon trajectories can be used as a useful and crucial tool to probe the thermodynamic black holes criticality.

Photon sphere and reentrant phase transition of charged Born-Infeld-AdS black holes

In this paper, we extend the study of the relationship between the photon sphere and the thermodynamic phase transition, especially the reentrant phase transition, to this black hole background. According to the number of the thermodynamic critical points, the black hole systems are divided into four cases with different values of Born-Infeld parameter b, where the black hole systems can have no phase transition, reentrant phase transition, or Van der Waals-like phase transition. For these different cases, we obtain the corresponding phase structures in pressure-temperature diagram and temperature-specific volume diagram. The tiny differences between these cases are clearly displayed. On the other hand, the radius rps and the minimal impact parameter ups of the photon sphere are calculated via the effective potential of the radial motion of photons. For different cases, rps and ups are found to have different behaviors. In particular, with the increase of rps or ups, the temperature possesses a decrease-increase-decrease-increase behavior for fixed pressure if there exists the reentrant phase transition. While for fixed temperature, the pressure will show an increase-decrease-increase-decrease behavior instead. These behaviors are quite different from that of the Van der Waals-like phase transition. Near the critical point, the changes of rps and ups among the black hole phase transition confirm an universal critical exponent 12. Therefore, all the results indicate that, for the charged Born-Infeld-AdS black holes, not only the Van der Waals-like phase transition, but also the reentrant phase transition can be reflected through the photon sphere.

Tricritical point and solid/liquid/gas phase transition of higher dimensional AdS black hole in massive gravity

By considering the fifth order graviton term in massive gravity theory, we study the P–V critical behaviors of AdS black hole in d≥7 dimensional space–time, and find the solid/liquid/gas phase transition with the “common” tricritical point, which does not exist in absence of higher graviton terms. Moreover, we also find the number of positive real roots of critical radius equation plays a key role in classifying different kinds of phase transitions. If there is only one positive root of equation, the first order Van der Waals-like phase transition emerges. For two roots, the system could experience a zero-order reentrant phase transition. Notably, for three roots, the solid/liquid/gas phase transition can occur. In addition, because the critical radius equation is a (n−2)-order polynomial equation associated with the graviton terms, the critical phenomena of black holes in extended phase space depend crucially on the number n of the graviton terms in high dimensional massive gravity.

Thermodynamics and phase transition of a nonlinear electrodynamics black hole in a cavity

We first discuss the thermodynamics of a Born-Infeld (BI) black hole enclosed in a finite spherical cavity. A canonical ensemble is considered, which means that the temperature and the charge on the wall of the cavity are fixed. After the free energy is obtained by computing the Euclidean action, it shows that the first law of thermodynamics is satisfied at the locally stationary points of the free energy. The phase structure and transition in various regions of the parameter space are then investigated. In the region where the BI electrodynamics has weak nonlinearities, Hawking-Page-like and van der Waals-like phase transitions occur, and a tricritical point appears. In the region where the BI electrodynamics has strong enough nonlinearities, only Hawking-Page-like phase transitions occur. The phase diagram of a BI black hole in a cavity can have dissimilarity from that of a BI black hole using asymptotically anti-de Sitter boundary conditions. The dissimilarity may stem from a lack of an appropriate reference state with the same charge and temperature for the BI-AdS black hole.

Quasinormal modes and van der Waals-like phase transition of charged AdS black holes in Lorentz symmetry breaking massive gravity

Using the quasinormal modes of a massless scalar perturbation, we investigate the small/large black hole phase transition in the Lorentz symmetry breaking massive gravity. We mainly focus on two issues: (i) the sign change of slope of the quasinormal mode frequencies in the complex-[Formula: see text] diagram; (ii) the behaviors of the imaginary part of the quasinormal mode frequencies along the isobaric or isothermal processes. For the first issue, our result shows that, at low fixed temperature or pressure, the phase transition can be probed by the sign change of slope. While increasing the temperature or pressure to certain values near the critical point, there will appear the deflection point, which indicates that such method may not be appropriate to test the phase transition. In particular, the behavior of the quasinormal mode frequencies for the small and large black holes tend to be the same at the critical point. For the second issue, it is shown that the nonmonotonic behavior is observed only when the small/large black hole phase transition occurs. Therefore, this property can provide us with an additional method to probe the phase transition through the quasinormal modes.