A unified picture of phase transition: from liquid-vapour systems to AdS black holes

TL;DR

This paper investigates phase transitions in AdS black holes using thermodynamic principles, confirming a second order transition between small and large black holes through Ehrenfest relations.

Contribution

It introduces a thermodynamic framework for analyzing second order phase transitions in AdS black holes, extending classical thermodynamics concepts to gravitational systems.

Findings

Black hole phase transition obeys Ehrenfest relations at critical point

Confirmed second order phase transition for rotating and charged AdS black holes

Analytical demonstration aligns black hole thermodynamics with classical phase transition theory

Abstract

Based on fundamental concepts of thermodynamics we examine phase transitions in black holes defined in Anti-de Sitter (AdS) spaces. The method is in line with that used a long ago to understand the liquid-vapour phase transition where the first order derivatives of Gibbs potential are discontinuous and Clausius-Clapeyron equation is satisfied. The idea here is to consider the AdS black holes as grand-canonical ensembles and study phase transition defined by the discontinuity of second order derivatives of Gibbs potential. We analytically check that this phase transition between the `smaller' and `larger' mass black holes obey Ehrenfest relations defined at the critical point and hence confirm a second order phase transition. This include both the rotating and charged black holes in Einstein gravity.