Second Order Phase Transition and Thermodynamic Geometry in Kerr-AdS Black Hole

TL;DR

This paper investigates second order phase transitions in Kerr-AdS black holes using Ehrenfest equations and thermodynamic geometry, revealing consistent second order behavior and connecting different analytical approaches.

Contribution

It introduces a scheme based on Ehrenfest equations to classify phase transitions in Kerr-AdS black holes and links this with thermodynamic geometry methods.

Findings

Phase transition is second order at fixed angular velocity.

Ehrenfest equations are satisfied during the transition.

Thermodynamic geometry results align with Ehrenfest analysis.

Abstract

We discuss a scheme based on Ehrenfest like equations to exhibit and classify transitions between two phases (with "smaller" and "larger" masses) of Kerr AdS black holes. We show that for fixed angular velocity this phase transition is of second order as both Ehrenfest's equations are satisfied. Finally we make a close connection of the results found from this analysis with those obtained from the thermodynamic state space geometry approach.