Thermodynamic Geometry and Phase Transitions in Kerr-Newman-AdS Black Holes

TL;DR

This paper explores the thermodynamic geometry of Kerr-Newman-AdS black holes, revealing how scalar curvature signals both second order and first order phase transitions, including liquid-gas like phenomena and phase coexistence.

Contribution

It demonstrates that the scalar curvature of thermodynamic state space encodes information about various phase transitions in black holes, extending previous understanding to new phase structures.

Findings

Scalar curvature diverges at second order critical points.

Scalar curvature indicates first order phase transitions and coexistence.

Black hole phase structures resemble Van der Waals liquid-gas behavior.

Abstract

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.