On the thermodynamics of the Hayward black hole

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 $l\approx0.333\,r_s$.