The description of phase transition of Bardeen black hole in the Ehrenfest scheme

TL;DR

This paper investigates the phase transition behavior of Bardeen black holes using Ehrenfest's scheme, revealing the occurrence of second order phase transitions through thermodynamic analysis.

Contribution

It provides a thermodynamic analysis of Bardeen black holes, demonstrating the presence of second order phase transitions via Ehrenfest's equations.

Findings

No first order phase transition due to continuous entropy and potential.

Second order phase transition indicated by heat capacity divergence.

Ehrenfest's equations satisfied at the transition point.

Abstract

The phase transition of a Bardeen black hole is studied by considering Ehrenfest's equations. The thermodynamic variables such as entropy, potential and heat capacity are calculated from the first law of thermodynamics for black holes. That no discontinuity in entropy and potential of the black holes means that the first order phase transition will not generate for the Bardeen black holes. However, the divergence of heat capacity at constant potential and satisfaction of the Ehrenfest's equations indicates that the second order phase transition of Bardeen black hole will appear.