On the thermodynamic geometry and critical phenomena of AdS black holes

Abstract

In this paper, we study various aspects of the equilibrium thermodynamic state space geometry of AdS black holes. We first examine the ReissnerNordstrom-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 KerrAdS 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. *

P − V criticality of charged AdS black holes

“…It turned out that the canonical ensemble admits a first order small-large black hole phase transition which is in many respects analogous to the liquid-gas phase transition in fluids. This triggered wide interest and various comparisons to the Van der Waals critical behaviour were studied, e.g., [22,[28][29][30] and references therein. In this appendix we recapitulate this interesting analogy and relate it to the results in the extended phase space performed in this paper.…”

Ehrenfest’s scheme and thermodynamic geometry in Born-Infeld AdS black holes

“…Finally, we apply the widely explored state space geometry approach [38]- [39] to analyze the phase transition phenomena in BI-AdS black holes [19]- [20], [40]- [51]. Our analysis reveals that the scalar curvature (R) diverges exactly at the critical points where C Φ diverges.…”

Phase transitions of hairy black holes in massive gravity and thermodynamic behavior of charged AdS black holes in an extended phase space

“…The first attempt in order to explore the thermodynamic properties [2,3] and instability of anti-de Sitter (AdS) black holes date back to the paper written by Hawking and Page [4]. Based on this successful idea, there have been several works addressing the critical behavior and nature of phase transitions related to black holes [5][6][7][8][9][10][11][12][13][14][15][16][17].…”