On the thermodynamics of the Hayward black hole

TL;DR

This paper investigates the thermodynamic properties of the Hayward black hole, analyzing its lapse function, phase transitions, and related thermodynamic variables, revealing a second order phase transition at a specific parameter value.

Contribution

It provides a detailed thermodynamic analysis of the Hayward black hole, including the role of the parameter l and the discovery of a phase transition.

Findings

Identification of the lapse function in terms of Schwarzschild radius and parameter l

Introduction of thermodynamic variables associated with l and the conjugate _H

Discovery of a second order phase transition at l  0.333 r_s

Abstract

In light of the growing interest in the Hayward black hole solution, a detailed study on the corresponding lapse function and its roots is presented. The lapse function is expressed in terms of the classical Schwarzschild radius $r_s$ and the Hayward's parameter $l$. Both of these quantities are used as thermodynamic variables to find related thermodynamic quantities. In this context, the variable $l$ is associated with a canonical conjugate variable $\mathcal{F}_H$, and a free energy $\Xi$. Moreover, a second order phase transition is found to appears at $l\approx0.333\,r_s$.