On the phase structure and thermodynamic geometry of R-charged black holes (original) (raw)
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Thermodynamic Geometry and Phase Transitions of Dyonic Charged AdS Black Holes
We investigate phase transitions and critical phenomena of four dimensional dyonic charged AdS black holes in the framework of thermodynamic geometry. In a mixed canonical grand canonical ensemble with a fixed electric charge and varying magnetic charge these black holes exhibit liquid gas like first order phase transition culminating in a second order critical point similar to the Van der Waals gas. We show that the thermodynamic scalar curvature R for these black holes follow our proposed geometrical characterization of the R-crossing Method for the first order liquid gas like phase transition and exhibits a divergence at the second order critical point. The pattern of R crossing and divergence exactly corresponds to those of a Van der Waals gas described by us in an earlier work.
Physics Letters B, 2017
It has been argued that charged Anti-de Sitter (AdS) black holes have similar thermodynamic behavior as the Van der Waals fluid system, provided one treats the cosmological constant as a thermodynamic variable (pressure) in an extended phase space. In this paper, we disclose the deep connection between charged AdS black holes and Van der Waals fluid system without extending the phase space. We keep the cosmological constant as a fixed parameter and instead, treat the square of the charge of black hole, Q 2 , as a thermodynamic variable. Therefore, we write the equation of state as Q 2 = Q 2 (T, Ψ) where Ψ (conjugate of Q 2) is the inverse of the specific volume, Ψ = 1/v. This allows us to complete the analogy of charged AdS black holes with Van der Waals fluid system and derive the phase transition as well as critical exponents of the system. We identify a thermodynamic instability in this new picture with real analogy to Van der Waals fluid with physically relevant Maxwell construction. We therefore study the critical behavior of isotherms in Q 2 − Ψ diagram and deduce all the critical exponents of the system and determine that the system exhibits a small-large black hole phase transition at the critical point (Tc, Q 2 c , Ψc). This alternative view is important as one can imagine such a change for a given single black hole i. e. acquiring charge which induces the phase transition. Finally, we disclose the microscopic properties of charged AdS black holes by using thermodynamic geometry. Interestingly, we find that scalar curvature has a gap between small and large black holes, and this gap becomes exceedingly large as one moves away from the critical point along the transition line. Therefore, we are able to attribute the sudden enlargement of the black hole to the strong repulsive nature of the internal constituents at the phase transition.
Geometrical thermodynamics of phase transition: charged black holes in massive gravity
In this paper, we study the stability conditions and phase transitions of charged black hole solutions in massive gravity. We point out the effects of massive parameter on stability conditions of these black holes and show how massive coefficients affect the phase transitions of these black holes. We also study the effects of boundary topology on thermodynamical behavior of the system. In addition, we give some arguments regarding the role of higher dimensions and highlight the effect of the charge in thermodynamical behavior. Then, we extend our study to geometrothermodynamical aspect of these solutions and show that employed approach for studying black holes geometrothermodynamics is an effective method.
Physical Review D, 2014
We study the thermodynamic behavior of static and spherically symmetric hairy black holes in massive gravity. In this case, the black hole is surrounded in a spherical cavity with a fixed temperature on the surface. It is observed that these black holes have a phase transition similar to the liquid-gas phase transition of a Van der Waals fluid. Also, by treating the cosmological constant Λ as a thermodynamic pressure P , we study the thermodynamic behavior of charged anti-de Sitter black holes in an ensemble with a pressure of P and an electric potential Φ as the natural variables. A second order phase transition is observed to take place for all the values of the electric potential Φ. * Electronic address: b.mirza@cc.iut.ac.ir † Electronic address: z.sherkat@ph.iut.ac.ir
Thermodynamic Geometry and Phase Transitions of AdS Braneworld Black Holes
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 structures on the braneworld parameter for these black holes.
Structure and thermodynamics of charged nonrotating black holes in higher dimensions
Physical Review D, 2019
We analyze the structural and thermodynamic properties of D-dimensional (D ≥ 4), asymptotically flat or anti-de Sitter, electrically charged black hole solutions, resulting from the minimal coupling of general nonlinear electrodynamics to general relativity. This analysis deals with static spherically symmetric (elementary) configurations with spherical horizons. Our methods are based on the study of the behavior (in vacuum and on the boundary of their domain of definition) of the Lagrangian density functions characterizing the nonlinear electrodynamic models in flat spacetime. These functions are constrained by some admissibility conditions endorsing the physical consistency of the corresponding theories, which are classified in several families, some of them supporting elementary solutions in flat space that are nontopological solitons. This classification induces a similar one for the elementary black hole solutions of the associated gravitating nonlinear electrodynamics, whose geometrical structures are thoroughly explored. A consistent thermodynamic analysis can be developed for the subclass of families whose associated black hole solutions behave asymptotically as the Schwarzschild metric (in the absence of a cosmological term). In these cases we obtain the behavior of the main thermodynamic functions, as well as important finite relations among them. In particular, we find the general equation determining the set of extreme black holes for every model, and a general Smarr formula, valid for the set of elementary black hole solutions of such models. We also consider the one-parameter group of scale transformations, which are symmetries of the field equations of any nonlinear electrodynamics in flat spacetime. These symmetries are respected by the minimal coupling to gravitation and induce representations of the group in the spaces of solutions of the different models, characterized by their thermodynamic functions. Exploiting this fact we find the expression of the equation of state of the set of black hole solutions associated with any model. These results are generalized to asymptotically anti-de Sitter solutions.
Thermodynamic geometry of black holes in the canonical ensemble
Physical review, 2018
We investigate the phase structure and critical phenomena for four dimensional Reissner-Nordström-AdS and Kerr-AdS black holes in the canonical ensemble, both for the normal and the extended phase space employing the framework of thermodynamic geometry. The thermodynamic scalar curvatures for these black holes characterize the liquid-gas-like first order phase transition analogous to the van der Waals fluids, through the R-Crossing method. It is also shown that the thermodynamic scalar curvatures diverge as a function of the temperature at the second order critical point.
Thermodynamic phase structure of charged anti-de Sitter scalar-tensor black holes
Journal of Physics: Conference Series, 2013
In the present paper we numerically construct new charged anti-de Sitter black holes coupled to nonlinear Born-Infeld electrodynamics within a certain class of scalar-tensor theories. The properties of the solutions are investigated both numerically and analytically. We also study the thermodynamics of the black holes in the canonical ensemble. For large values of the Born-Infeld parameter and for a certain interval of the charge values we find the existence of a first-order phase transition between small and very large black holes. An unexpected result is that for a certain small charge subinterval two phase transitions have been observed, one of zeroth and one of first order. It is important to note that such phase transitions are also observed for pure Einstein-Born-Infeld-AdS black holes. *
Universal criticality of thermodynamic curvatures for charged AdS black holes
Physical Review D, 2020
In this paper, we analytically study the critical exponents and universal amplitudes of the thermodynamic curvatures such as the intrinsic and extrinsic curvature at the critical point of the small-large black hole phase transition for the charged AdS black holes. At the critical point, it is found that the normalized intrinsic curvature R N and extrinsic curvature K N has critical exponents 2 and 1, respectively. Based on them, the universal amplitudes R N t 2 and K N t are calculated with the temperature parameter t = T /T c − 1 where T c the critical value of the temperature. Near the critical point, we find that the critical amplitude of R N t 2 and K N t is − 1 2 when t → 0 + , whereas R N t 2 ≈ − 1 8 and K N t ≈ − 1 4 in the limit t → 0 −. These results not only hold for the four dimensional charged AdS black hole, but also for the higher dimensional cases. Therefore, such universal properties will cast new insight into the thermodynamic geometries and black hole phase transitions.