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Register a new userThermodynamic Geometry and Phase Transitions of AdS Braneworld Black Holes
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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.
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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.
We investigate phase transitions and critical phenomena in Kerr-Newman-Anti de Sitter black holes in the framework of the geometry of their equilibrium thermodynamic state space. The scalar curvature of these state space Riemannian geometries is computed in various ensembles. The scalar curvature diverges at the critical point of second order phase transitions for these systems. Remarkably, however, we show that the state space scalar curvature also carries information about the liquid-gas like first order phase transitions and the consequent instabilities and phase coexistence for these black holes. This is encoded in the turning point behavior and the multi-valued branched structure of the scalar curvature in the neighborhood of these first order phase transitions. We re-examine this first for the conventional Van der Waals system, as a preliminary exercise. Subsequently, we study the Kerr-Newman-AdS black holes for a grand canonical and two mixed ensembles and establish novel phase structures. The state space scalar curvature bears out our assertion for the first order phase transitions for both the known and the new phase structures, and closely resembles the Van der Waals system.
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 diagram to study the thermodynamics of the charged Kerr-AdS black hole. This shows that the qualitative phase structures agree between the both sides. We also find that the ratio of the thermodynamical quantities is almost well-known factor 3/4 even at the low temperature.
In this paper, we study various aspects of the equilibrium thermodynamic state space geometry of AdS black holes. We first examine the Reissner-Nordstrom-AdS (RN-AdS) and the Kerr-AdS black holes. In this context, the state space scalar curvature of these black holes is analysed in various regions of their thermodynamic parameter space. This provides important new insights into the structure and significance of the scalar curvature. We further investigate critical phenomena, and the behaviour of the scalar curvature near criticality, for KN-AdS black holes in two mixed ensembles, introduced and elucidated in our earlier work arXiv:1002.2538 [hep-th]. The critical exponents are identical to those in the RN-AdS and Kerr-AdS cases in the canonical ensemble. This suggests an universality in the scaling behaviour near critical points of AdS black holes. Our results further highlight qualitative differences in the thermodynamic state space geometry for electric charge and angular momentum fluctuations of these.
We consider a generic first-order phase transition at finite temperature and investigate to what extent a population of primordial black holes, of variable masses, can affect the rate of bubble nucleation. Using a thin-wall approximation, we construct the Euclidean configurations that describe transition at finite temperature. After the transition, the remnant black hole mass is dictated dynamically by the equations of motion. The transition exponent is computed and displays an explicit dependence on temperature. We find the configuration with the lowest Euclidean action to be static and $O(3)$ symmetric; therefore, the transition takes place via thermal excitation. The transition exponent exhibits a strong dependence on the seed mass black hole, $M_+$, being almost directly proportional. A new nucleation condition in the presence of black holes is derived and the nucleation temperature is compared to the familiar flat-space result, i.e. $S_3/T$. For an electroweak-like phase transition it is possible to enhance the nucleation rate if $M_+ lesssim 10^{15} M_{rm P}$. Finally, we outline the possible transition scenarios and the consequences for the power spectrum of stochastic gravitational waves produced due to the first-order phase transition.
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