On the Thermodynamic Geometry and Critical Phenomena of AdS Black Holes

TL;DR

This paper explores the thermodynamic geometry of AdS black holes, analyzing scalar curvature and critical phenomena to reveal universal scaling laws and differences in state space structure for various black hole types.

Contribution

It provides new insights into the thermodynamic geometry of AdS black holes, including analysis of scalar curvature and critical behavior across different ensembles and black hole types.

Findings

Scalar curvature analysis reveals structure of black hole thermodynamics.

Critical exponents show universality across different AdS black holes.

Qualitative differences in state space geometry for charge and angular momentum fluctuations.

Abstract

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.