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Register a new userThermodynamic Geometry of Black Holes in the Canonical Ensemble
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We investigate the thermodynamics and critical phenomena for four dimensional RN-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 characterizes 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 critical point.
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Thermodynamic fluctuation metrics in Ruppeiners formalism are worked out for Kerr-AdS black holes in the extended state space. The implications of constraints upon the state space geometry and their correspondence with thermodynamical ensembles are explicitly worked out in the most general setting. The state space scalar curvature for a given ensemble is found to be sensitive to the instabilities/phase transitions therein. In particular, it is found that the appropriate Ruppeiner scalar curvature does encode critical phenomena in the Kerr-AdS black holes. A detailed study is undertaken of the curvature contour of the state space of the 4d Kerr-AdS black hole and suitable inferences are drawn. In particular, thermodynamic geometry suggests an instability in the Schwarzschild-AdS limit for all the ensembles except the pressure ensemble which is equivalent to the unextended state space of the Kerr-AdS black holes. The extrinsic geometry of the ensemble hypersurfaces is introduced and its relevance to constrained thermodynamic fluctuations discussed. A new interpretation for the thermodynamic curvature of black hole systems is suggested.
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.
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.
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 the phase structure and equilibrium state space geometry of R-charged black holes in $D = 5$, 4 and 7 and the corresponding rotating $D3$, $M2$ and $M5$ branes. For various charge configurations of the compact black holes in the canonical ensemble we demonstrate new liquid-gas like phase coexistence behaviour culminating in second order critical points. The critical exponents turn out to be the same as that of four dimensional asymptotically AdS black holes in Einstein Maxwell theory. We further establish that the regions of stability for R-charged black holes are, in some cases, more constrained than is currently believed, due to properties of some of the response coefficients. The equilibrium state space scalar curvature is calculated for various charge configurations, both for the case of compact as well as flat horizons and its asymptotic behaviour with temperature is established.
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