In this paper, we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space. It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity, the charged AdS black hole also admits an van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume. Based on this, we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework. On the one hand, we give the phase diagram structures of the charged AdS black hole accurately and analytically, which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity. On the other hand, we analyse the thermodynamic curvature of the black hole in two coordinate spaces. The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive. Based on an empirical conclusion under the framework of thermodynamic geometry, we speculate that when the square of charge is treated as an independent thermodynamic quantity, the charged AdS black hole is likely to present a repulsive between its molecules. More importantly, based on the thermodynamic curvature, we obtain an universal exponent at the critical point of phase transition.
In this note, we consider the equations of motion for charged branes in AdS space and show that they can be cast into one-dimensional coupled Toda type. Then we solve the equations of motion to construct static charged AdS brane solutions which are invariant under translation along $p$ directions and have toroidal symmetry. The solutions are described by mass, charges and a dilaton coupling constant.
We numerically construct charged boson stars in asymptotically AdS spacetime. We find an intricate phase diagram dominated by solutions whose main matter contribution are alternately provided by the scalar field or by the gauge field.
The thermodynamics and phase transitions of charged RN-AdS and rotating Kerr-AdS black holes in a generalized Randall-Sundrum braneworld are investigated in the framework of thermodynamic geometry. A detailed analysis of the thermodynamics, stability and phase structures in the canonical and the grand canonical ensembles for these AdS braneworld black holes are described. The thermodynamic curvatures for both these AdS braneworld black holes are computed and studied as a function of the thermodynamic variables. Through this analysis we illustrate an interesting dependence of the phase structur…
We study thermodynamic and classical instability of AdS black holes in fourth-order gravity. These include the BTZ black hole in new massive gravity, Schwarzschild-AdS black hole, and higher-dimensional AdS black holes in fourth-order gravity. All thermodynamic quantities which are computed using the Abbot-Deser-Tekin method are used to study thermodynamic instability of AdS black holes. On the other hand, we investigate the $s$-mode Gregory-Laflamme instability of the massive graviton propagating around the AdS black holes. We establish the connection between the thermodynamic instability and…
In this work we study the phase transitions between the planar charged AdS black hole and the planar charged soliton. The planar soliton is obtained as a double analytic continuation of the charged black hole metric, which also involves analytically continuing the electric charge. We show that there are phase transitions between both solutions depending on the electric potential, magnetic flux and temperature. The analysis is carried out in the Grand-Canonical ensemble.
In this paper, we consider a charged rotating AdS black holes in four dimensions and study the effects of leading-order thermal corrections on the thermodynamics of such system explicitly. The first-order corrected thermodynamical quantities also satisfy the first-law of thermodynamics of the black holes. The holographic duality between the charged rotating AdS black holes and Van der Waals fluid is also emphasized through the $P-v$ diagram. Finally, we study the effects of the leading-order thermal corrections on the stability of the charged rotating black holes.
We study the thermodynamic properties of the RN-AdS black hole in full phase space and propose a generalized thermodynamic identity. As an example, we use it to find relations of thermodynamical coefficients between the grand canonical and canonical ensembles. We also show, for the first order phase transition, that the usual Maxwell's equal area law should be extended to a new form for the RN-AdS black hole.
We present a new family of topological charged hairy black hole solutions in asymptotically AdS space in $D$-dimensions. We solve the coupled Einstein-Maxwell-Scalar gravity system and obtain exact charged hairy black hole solutions with planar, spherical and hyperbolic horizon topologies. The scalar field is regular everywhere. We discuss the thermodynamics of the hairy black hole and find drastic changes in its thermodynamic structure due to the scalar field. For the case of planar and spherical horizons, we find charged hairy/RN-AdS black hole phase transition, with thermodynamically prefer…
As an intriguing topological defect, global monopole's influence on behaviors of black holes has always been anticipated but still remains less clear. Analyzing the thermodynamics of charged AdS black hole incorporating a global monopole manifests that the black hole undergoes a first-order phase transition at critical point, and of special interest, the critical behaviors qualitatively resemble a Van der Waals liquid-gas system. This paper concentrates on further investigating the charged AdS black hole with a global monopole, aiming at clarifying the significant effects of the global monopol…
We study electromagnetically charged dilatonic black brane solutions in arbitrary dimensions with flat transverse spaces, that are asymptotically AdS. This class of solutions includes spacetimes which possess a bulk region where the metric is approximately invariant under Lifshitz scalings. Given fixed asymptotic boundary conditions, we analyze how the behavior of the bulk up to the horizon varies with the charges and derive the extremality conditions for these spacetimes.
We study the thermodynamics in the grand canonical ensemble of D-dimensional charged Gauss-Bonnet-AdS black holes in the extended phase space. We find that the usual small-large black hole phase transition, which exhibits analogy with the Van de Waals liquid-gas system holds in five-dimensional spherical charged Gauss-Bonnet-AdS black holes when its potential is fixed within the range $0<Φ<\frac{\sqrt{3}π}{4}$. For the other higher dimensional and topological charged Gauss-Bonnet-AdS black holes, there is no such phase transition. In the limiting case, Reissner-Nordstrom-AdS black holes, with …
A new formalism for thermodynamics of AdS black holes called the {\em restricted phase space thermodynamics} (RPST) is proposed. The construction is based on top of Visser's holographic thermodynamics, but with the AdS radius fixed as a constant. Thus the RPST is free of the $(P,V)$ variables but inherits the central charge and chemical potential as a new pair of conjugate thermodynamic variables. In this formalism, the Euler relation and the Gibbs-Duhem equation hold simultaneously with the first law of black hole thermodynamics, which guarantee the appropriate homogeneous behaviors for the b…
We generalize the vacuum static black brane solutions of Einstein's equations with negative cosmological constant recently discussed in literature, by introducing rotations and an electromagnetic field. We investigate numerically the thermodynamical properties of the charged and of the rotating $AdS$ black brane and we provide evidences for the existence of the charged and rotating case. In particular, we study the influence of the rotation and charge on the tension and mass. We find that the rotation essentially influences the tensions while the charge essentially influences the mass.
We investigate the holographic entanglement entropy in the Rindler-AdS space-time to obtain an exact solution for the corresponding minimal surface. Moreover, the holographic entanglement entropy of the charged single accelerated AdS Black holes in four dimensions is investigated. We obtain the volume of the codimension one-time slice in the bulk geometry enclosed by the minimal surface for both the RindlerAdS space-time and the charged accelerated AdS Black holes in the bulk. It is shown that the holographic entanglement entropy and the volume enclosed by the minimal hyper-surface in both the…
We study thermodynamics and thermodynamic geometry of a five-dimensional Schwarzschild AdS black hole in $AdS_5\times{S^5}$ spacetime by treating the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. It is found that the chemical potential is always negative in the stable branch of black hole thermodynamics and it has a chance to be positive, but appears in the unstable branch. We calculate scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric and Quevedo metric, respectively and we f…
In this paper, we show the relation between the thermodynamic geometry of a four-dimensional Reissner-Nordstrom-AdS (RN-AdS) black hole and non-local observables in boundary field theory. Instead of introducing the critical point associating with the black hole charge to nondimensionalize the thermodynamics parameters, we use the cosmological constant to rescale these variables, so that a universal specific equation of state of the black hole is obtained. Further, the correspondence between thermodynamic properties of the black hole and the oscillating behaviors of the non-local observables ha…
Treating the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the critical behaviour of charged AdS black holes. We complete the analogy of this system with the liquid-gas system and study its critical point, which occurs at the point of divergence of specific heat at constant pressure. We calculate the critical exponents and show that they coincide with those of the Van der Waals system.
A large AdS Schwarzschild black hole can be approximated by an AdS planar black hole. However, the temperature of a planar black hole is not well defined due to the translational invariance of the horizon. We propose to fix this arbitrariness by imposing the entropy area law. Furthermore, using the AdS/CFT holography, we propose a relationship between the temperatures of an AdS planar and large AdS Schwarzschild black holes.
In this letter we investigate the throttling process of the charged Anti-de Sitter (AdS) black holes in the rainbow gravity. In the extended phase space of these black holes, the cosmological constant plays the role of a varying thermodynamic pressure and the black hole mass is identified with the thermodynamic enthalpy. We derive exact expressions for the Joule-Thomson coefficient and the inversion temperature in terms of black hole parameters and constants of rainbow gravity analytically, and then perform a numerical analysis for the isenthalpic and inversion curves of charged AdS black hole…
The Ruppeiner geometry and the fluctuation for a four-dimensional charged AdS black hole in the framework of the extensive thermodynamics have been investigated. By fixing the AdS radius of Vissers construction, the extensive thermodynamics of the RN-AdS black hole is established, and the central charge plays the role of particle number. With the thermodynamic variables density, we reexamine the phase transition of the black hole, and the result will hold for the black holes under different gravitational models. Moreover, we have studied the Ruppeiner geometry and the black hole fluctuation, a…
In this paper, we will analyze the effects of thermal fluctuations on a charged AdS black hole. This will be done by analyzing the corrections to black hole thermodynamics due to these thermal fluctuations. We will demonstrate that the entropy of this black hole get corrected by logarithmic term. We will also calculate other corrections to other important thermodynamic quantities for this black hole. Finally, we will use the corrected value of the specific heat to analyze the phase transition in this system.
We study the thermodynamics and the phase structures of Reissner-Nordstrom and Born-Infeld black holes in AdS space by constructing ``off-shell'' free energies using thermodynamic quantities derived directly from the action. We then use these results to propose ``off-shell'' effective potentials for the respective boundary gauge theories. The saddle points of the potentials describe all the equilibrium phases of the gauge theories.
We consider leading order quantum corrections to the geometry of large AdS black holes in a spherical reduction of four-dimensional Einstein gravity with negative cosmological constant. The Hawking temperature grows without bound with increasing black hole mass, yet the semiclassical back-reaction on the geometry is relatively mild, indicating that observers in free fall outside a large AdS black hole never see thermal radiation at the Hawking temperature. The positive specific heat of large AdS black holes is a statement about the dual gauge theory rather than an observable property on the gr…
The extended thermodynamics of static charged AdS black holes in conformal gravity is analyzed. The $P-V$ criticality of these black holes has some unusual features. There exists a single critical point with critical temperature $T_c$ and critical pressure $P_c$. At fixed $T>T_c$ (or at fixed $P>P_c$), there are two zeroth order phase transition points but no first order phase transition points. The systems favors large pressure states at constant $T$, or high temperature states at constant $P$.
Employing the thermodynamic geometry approach, we explore phase transition of four dimensional spinning black holes in an anti-de Sitter (AdS) spaces and found the following novel results. (i) Contrary to the charged AdS black hole, thermodynamic curvature of the spinning AdS black hole diverges at the critical point, without needing normalization.(ii) There is a certain region with small entropy in the space of parameters for which the thermodynamic curvature is positive and the repulsive interaction dominates. Such behavior exists even when the pressure is extremely large. (iii) The dominant…
In theories of semi-classical quantum gravity where the cosmological constant is considered a thermodynamic variable, the gravitational mass of a black hole has been shown to correspond to the enthalpy of the thermodynamic system, rather than the energy. We propose that this should be extended to all spacetime solutions, and consider the meaning of this extension of gravitational thermodynamics for the Taub-NUT and Taub-Bolt geometries in four dimensional locally anti-de Sitter spacetime. We present formulae for their thermodynamic volumes. Surprisingly, Taub-NUT has negative volume, for which…
In theories of gravity where the cosmological constant defines a thermodynamic variable, the pressure, it has been shown that solutions of Einstein's equations have a corresponding thermodynamic volume. In general, the expression for the volume is not the same as the one arising from naive geometrical considerations. Both rotation and nut charge are properties known in the literature to give non-geometric thermodynamic volumes, and so we combine the two in a single example and compute the volume for the Kerr-bolt-AdS spacetime, presenting a new expression that generalizes the previously known …
The thermodynamics of the Schwarzschild-AdS black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Different choices of the metric in the equilibrium states manifold are used in order to reproduce the Hawking-Page phase transition as a divergence of the thermodynamical curvature scalar. We show that the enthalpy and total energy representations of GTD does not reproduce the transition while the entropy rep- resentation gives the expected behavior.
Topological classes of thermodynamics of the static multi-charge AdS black holes in gauged supergravities: novel temperature-dependent thermodynamic topological phase transition
Due to the non-independence of entropy and thermodynamic volume for spherically symmetric black holes in the AdS spacetime, when applying the Ruppeiner thermodynamic geometry theory to these black holes, we often encounter an unavoidable problem of the singularity about the line element of thermodynamic geometry. In this paper, we propose a basic and natural scheme for dealing with the thermodynamic geometry of spherically symmetric AdS black holes. We point out that enthalpy, not internal energy, is the fundamental thermodynamic characteristic function for the Ruppeiner thermodynamic geometry…
We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a $D$-dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a $(D-2)$-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermod…
Recently, black hole thermodynamics and phase transition have been studied in the extended phase space. Besides the VdW-like phase transition, more interesting phase transitions were found. More interestingly, combining with the thermodynamic geometry, the microstructure of black holes was investigated.In this paper, we give a brief review of recent progress on this subject.
Using the AdS/CFT, we establish a correspondence between the intricate thermal phases of R-charged AdS_{5} blackholes and the R-charge sector of the N=4 gauge theory, in the large N limit. Integrating out all fields in the gauge theory except the thermal Polyakov line, leads to an effective unitary matrix model. In the canonical ensemble, a logarithmic term is generated in the non-zero charge sector of the matrix model. This term is important to discuss various supergravity properties like i) the non-existence of thermal AdS as a solution, ii) the existence of a point of cusp catastrophe in th…
When an electrically charged black hole is perturbed its inner horizon becomes a singularity, often referred to as the Poisson-Israel mass inflation singularity. Ori constructed a model of this phenomenon for asymptotically flat black holes, in which the metric can be determined explicitly in the mass inflation region. In this paper we implement the Ori model for charged AdS black holes. We find that the mass function inflates faster than the flat space case as the inner horizon is approached. Nevertheless, the mass inflation singularity is still a weak singularity: although spacetime curvatur…
We investigate the relations between the black hole shadow and charged AdS black hole critical behaviour in the extended phase space. Using the thermo-shadow formalism built-in [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 th…
The super-entropic black hole, which possesses a noncompact horizon topology and violates the reverse isoperimetric inequality, has been found to satisfy both the thermodynamic first law and the Bekenstein-Smarr mass formula. In this paper, we first derive a new Christodoulou-Ruffini-like squared-mass formula for the four-dimensional Kerr-Newman-AdS super-entropic black hole, and then establish a set of very simple relations between thermodynamic quantities of the super-entropic Kerr-Newman-AdS$_4$ black hole and its usual counterparts. Using these relations, the thermodynamic quantities of th…
In this paper, we consider dyonic charged AdS black hole which is holographic dual of a van der Waals fluid. We use logarithmic corrected entropy and study thermodynamics of the black hole and show that holographic picture is still valid. Critical behaviors and stability also discussed. Logarithmic corrections arises due to thermal fluctuations which are important when size of black hole be small. So, thermal fluctuations interpreted as quantum effect. It means that we can see quantum effect of a black hole which is a gravitational system.
Motivated by a recent work on asymptotically Ad$S_4$ black holes in M-theory, we investigate both thermodynamics and thermodynamical geometry of Raissner-Nordstrom-AdS black holes from M2-branes. More precisely, we study AdS black holes in $AdS_{4}\times S^{7}$, with the number of M2-branes interpreted as a thermodynamical variable. In this context, we calculate various thermodynamical quantities including the chemical potential, and examine their phase transitions along with the corresponding stability behaviors. In addition, we also evaluate the thermodynamical curvatures of the Weinhold, Ru…
We investigate the conjectured bound on the Lyapunov exponent for a charged particle with angular motion in the Kerr-Newman-AdS black hole. The Lyapunov exponent is calculated based on the effective Lagrangian. We show that the negative cosmological constant reduces the chaotic behavior of the particle, namely, it decreases the Lyapunov exponent. Hence, the bound is more effective in the AdS spacetime than in the flat spacetime. Nevertheless, we find that the bound can be violated when the angular momenta of the black hole are turned on. Moreover, we show that in an extremal black hole, the bo…
Thermodynamics of Bardeen AdS black holes has attracted a great deal of attentions due to its intrinsic complications and rich phase structures. However, the entropy and thermodynamic volume are incorrect in some literatures. In this paper we revisit the thermodynamics of Bardeen AdS black holes and provide the correct entropy and thermodynamic volume. Furthermore, thermodynamic geometries are a powerful tool to probe the microstructure of black holes. Based on the Hessian matrix of black hole mass, we introduce a thermodynamic metric and give its scalar curvature in Weinhold's geometry. The c…
Recently Gibbons {\it et al.} in hep-th/0408217 defined a set of conserved quantities for Kerr-AdS black holes with the maximal number of rotation parameters in arbitrary dimension. This set of conserved quantities is defined with respect to a frame which is non-rotating at infinity. On the other hand, there is another set of conserved quantities for Kerr-AdS black holes, defined by Hawking {\it et al.} in hep-th/9811056, which is measured relative to a frame rotating at infinity. Gibbons {\it et al.} explicitly showed that the quantities defined by them satisfy the first law of black hole the…
We reconsider the thermodynamics of AdS black holes in the context of gauge-gravity duality. In this new setting where both the cosmological constant $Λ$ and the gravitational Newton constant $G$ are varied in the bulk, we rewrite the first law in a new form containing both $Λ$ (associated with thermodynamic pressure) and the central charge $C$ of the dual CFT theory and their conjugate variables. We obtain a novel thermodynamic volume, in turn leading to a new understanding of the Van der Waals behavior of the charged AdS black holes, in which phase changes are governed by the degrees of free…
The thermodynamic geometry has been proved to be quite useful in understanding the microscopic structure of black holes. We investigate the phase structure, thermodynamic geometry and critical behavior of a Reissner-Nordstrom-AdS black hole and a Reissner-Nordstrom black hole in a cavity, which can reach equilibrium in a canonical ensemble. Although the phase structure and critical behavior of both cases show striking resemblance, we find that there exist significant differences between the thermodynamic geometry of these two cases. Our results imply that there may be a connection between the …
We obtain spherically-symmetric and $\R^2$-symmetric dyonic black holes that are asymptotic to anti-de Sitter space-time (AdS), which are solutions in maximal gauged four-dimensional supergravity, with just one of the U(1) fields carrying both the electric and magnetic charges $(Q,P)$. We study the thermodynamics, and find that the usually-expected first law does not hold unless P=0, Q=0 or P=Q. For general values of the charges, we find that the first law requires a modification with a new pair of thermodynamic conjugate variables. We show that they describe the scalar hair that breaks some o…
We obtain the charged rotating black hole in conformal gravity. The metric is asymptotic to the (anti-)de Sitter spacetime. The contribution to the metric from the charges has a slower falloff than that in the Kerr-Newman AdS black hole. We analyse the global structure and obtain all the thermodynamical quantities including the mass, angular momentum, electric/magnetic charges and their thermodynamical conjugates. We verify that the first law of thermodynamics holds. We also obtain the new neutral rotating black holes that are beyond Einstein metrics. In contrast to the static ones, these rota…
We consider the geometry of anti-de-Sitter (AdS) black hole thermodynamics in four dimensions, where the equation of state in the extended phase space formalism allows explicit comparison with normal fluid systems. We show that for the two-dimensional parameter manifolds considered here, the scalar curvature is proportional to the thermodynamic volume. This allows us to critically examine the applicability of geometric methods in black hole thermodynamics in extended phase space. We show how several standard features that are expected to hold in normal fluid systems impose severe restrictions …
We study N =4 super Yang-Mills theories on a three sphere with two kinds of chemical potentials. One is associated with the R-symmetry and the other with the rotational symmetry of S^3 (SO(4) symmetry). These correspond to the charged Kerr-AdS black holes via AdS/CFT. The exact partition functions at zero coupling are computed and the thermodynamical properties are studied. We find a nontrivial gap between the confinement/deconfinement transition line and the boundary of the phase diagram when we include more than four chemical potentials. In the dual gravity, we find such a gap in the phase d…
We calculate the quasinormal modes of massless scalar perturbations around small and large four-dimensional Reissner-Nordstrom-Anti de Sitter (RN-AdS) black holes. We find a dramatic change in the slopes of quasinormal frequencies in small and large black holes near the critical point where the Van der Waals like thermodynamic phase transition happens. This further supports that the quasinormal mode can be a dynamic probe of the thermodynamic phase transition.
We investigate the thermodynamics of phase transition for $ (n+1) $ dimensional Reissner Nordstrom (RN)-AdS black holes using a grand canonical ensemble. This phase transition is characterized by a discontinuity in specific heat. The phase transition occurs from a lower mass black hole with negative specific heat to a higher mass black hole with positive specific heat. By exploring Ehrenfest's scheme we show that this is a second order phase transition. Explicit expressions for the critical temperature and critical mass are derived. In appropriate limits the results for $ (n+1) $ dimensional S…
Extending researches on Hawking radiation to conformal gravity theory, we discuss Hawking radiation of different particles across charged rotating AdS black holes in conformal gravity, including charged massive particles, complex scalar and spin-$1/2$ Dirac particles. To make the study of rotating black holes' tunneling radiation get rid of the dependence on dragging coordinate systems, we investigate the radiation without dragging coordinate transformations. The previous geodesic derivation existed some shortcomings. Not only did geodesics of massive and massless particles are derived by usin…
Herein, we focus on the study of Joule-Thomson expansion corresponding to a d-dimensional charged AdS black hole with cloud of strings and quintessence. Then its relevant solution and some thermodynamic properties are investigated. Specifically, we evaluate its Joule-Thomson expansion from four important aspects, including the Joule-Thomson coefficient, inversion curve, isenthalpic curve, and ratio $\frac{T_{i}^{min}}{T_{c}}$. After analysis, different dimensions with strings of cloud and quintessence parameters have different effects on the Joule-Thomson coefficient (the same situation are fo…
We consider quantum field theory near the horizon of an extreme Kerr black hole. In this limit, the dynamics is well approximated by a tower of electrically charged fields propagating in an $SL(2,\mathbb{R})$ invariant AdS$_2$ geometry endowed with a constant, symmetry preserving background electric field. At large charge the fields oscillate near the AdS$_2$ boundary and no longer admit a standard Dirichlet treatment. From the Kerr black hole perspective, this phenomenon is related to the presence of an ergosphere. We discuss a definition for the quantum field theory whereby we 'UV' complete …
