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

TL;DR

This paper investigates second order phase transitions in Born-Infeld AdS black holes through Ehrenfest's thermodynamic scheme and state space geometry, confirming the transition's nature and compatibility of methods.

Contribution

It provides an analytical verification of the second order phase transition in Born-Infeld AdS black holes using both Ehrenfest's scheme and thermodynamic geometry, which is a novel combined approach.

Findings

Phase transition is second order, confirmed by Ehrenfest's equations.

Divergences in heat capacity mark critical points.

Thermodynamic geometry analysis agrees with Ehrenfest's scheme.

Abstract

In this paper we analyze the phase transition phenomena in Born-Infeld AdS black holes using Ehrenfest's scheme of standard thermodynamics. The critical points are marked by the divergences in the heat capacity. In order to investigate the nature of the phase transition, we analytically check both the Ehrenfest's equations near the critical points. Our analysis reveals that this is indeed a second order phase transition. Finally, we analyze the nature of the phase transition using state space geometry approach. This is found to be compatible with the Ehrenfest's scheme.