We investigate the heat properties of AdS Black Holes in higher dimensions. We consider the study of the corresponding thermodynamical properties including the heat capacity explored in the determination of the black hole stability. In particular, we compute the heat latent. To overcome the instability problem, the Maxwell construction, in the (T, S)-plane, is elaborated. This method is used to modify the the Hawking-Page phase structure by removing the negative heat capacity regions. Then, we discuss the thermodynamic cycle and the heat engines using the way based on the extraction of the work from a black hole solution.

The principal focus of the present work concerns the critical behaviors of a class of three dimensional black holes with a scalar field hair. Since the cosmological constant is viewed as a thermodynamic pressure and its conjugate quantity as a volume, we examine such properties in terms of two parameters B and a. The latters are related to the scalar field and the angular momentum respectively. In particular, we give the equation of state predicting a critical universal number depending on the (B, a) moduli space. In the vanishing limit of the B parameter, we recover the usual perfect gas behavior appearing in the case of the non rotating BTZ black hole. We point out that in a generic region of the (B, a) moduli space, the model behaves like a Van der Waals system.

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare -Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

Motivated by recent work on asymptotically AdS 4 black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2-and M5-branes. Concretely, we consider AdS black holes in Ad S p+2 × S 11− p−2 , where p = 2, 5 by interpreting the number of M2-(and M5-branes) as a thermodynamical variable. More precisely, we study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then we compute the thermodynamical curvatures from the Quevedo metric for M2-and M5-branes geometries to reconsider the stability of such black holes. The Quevedo metric singularities recover similar stability results provided by the phase-transition program. It has been shown that similar behaviors are also present in the limit of large N .

In this work we use the quasinormal frequencies of a massless scalar perturbation to probe the phase transition of the high dimension charged AdS black hole. The signature of the critical behavior of this black hole solution is detected in the isobaric as well as in isothermal process. This paper is a natural generalization of Liu et al. (JHEP 1409(JHEP :179, 2014 to higher dimensional spacetime. More precisely our study shows a clear signal for any dimension d in the isobaric process. As to the isothermal case, we find that this signature can be affected by other parameters like the pressure and the horizon radius. We conclude that the quasinormal modes can be an efficient tool to investigate the first-order phase transition, but fail to disclose the signature of the second-order phase transition.

In this paper, we study Joule-Thomson expansion for charged AdS black holes in f (R) gravity. We obtain the inversion temperatures as well as inversion curves, and investigate similarities and differences between van der Waals fluids and charged AdS black holes in f (R) gravity for this expansion. In addition, we determine the position of the inversion point versus different values of the mass M , the charge Q and the parameter b for such black hole. At this point, the Joule-Thomson coefficient µ vanishes, an import feature that we used to obtain the cooling-heating regions by scrutinizing the sign of the µ quantity.Nowadays, an f (R) gravity is one of important class of the modified Einstein's gravity. In general, It is built through adding higher powers of the scalar curvature R, the Riemann and Ricci tensors, or their derivatives to the lagrangian description [1][2][3][4][5]. This kind of gravity mimics successfully the history of universe, especially the current cosmic acceleration, the inflation and structure formation in the early Universe [2,3], various extensions of f(R) gravity theory has been elaborated ranging from three dimensional [6] and asymptotically Lifshitz black hole solutions [7] to F(R) gravity's rainbow model [8].Recently, a special attention has been devoted to the study of the black holes phase transition particularly after the introduction of the notion of the extended phase space via the identification of the cosmological constant with the pressure and its conjugate quantity with thermodynamic volume [9]. In this context, the black hole behaves like Van der Waals fluid [10-12] leading to a remarkable correspondence between the thermal physics of black holes and simple substances [13]. Numerous extensions of these works have been elaborated for rotating and hairy black hole [14,15], high curvature theories of gravity and M-theory [16][17][18][19]. More exotic results as holographic heat engine [20] as well as other technics ranging from the behaviour of the quasi-normal modes [21,22] to AdS/CFT tools [23,24] and chaos structure [25] have consolidated the similarity with the Van der Waals fluid.Meanwhile, a considerable effort has been dedicated to explore the thermodynamics of the AdS black hole in the R + f (R) gravity background with a constant curvature [26] where the essential of thermodynamical quantities like the entropy, heat capacity and the Helmholtz free energy are calculated, then the extended phase space and the critical Van der Waals-like behavior introduced in [26,27] as well as the canonical ensembles in [28]. Here we would like to go further in the thermodynamical investigation and study the Joule-Thomson expansion for the charged-AdS black hole configuration in the f (R) gravity background.More recently, the authors of [29] have investigated the JT expansion for AdS charged black holes with the aim to confront the resulting features with those of Van der Waals fluids. The extension to rotating-AdS black hole [30] and the charged black hole solution in the presence of the ...

Interpreting the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we study the Maxwell equal-area law of higher dimensional Gauss-Bonnet-AdS black holes in extended phase space. These black hole solutions critically behave like van der Waals systems. It has been realized that below the critical temperature T c the stable equilibrium is violated. We show through calculations that the critical behaviors for the uncharged black holes only appear in d = 5. For the charged case, we analyze solutions in d = 5 and d = 6 separately and find that, up to some constraints, the critical behaviors only appear in the spherical topology. Using the Maxwell construction, we also find the isobar line for which the liquid-gas-like phases coexist.

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.