Remarks on nonsingular models of Hayward and magnetized black hole with rational nonlinear electrodynamics

A Hayward black hole and magnetically charged black hole based on rational nonlinear electrodynamics with the Lagrangian ${\cal L} = -{\cal F}/(1+2\beta{\cal F})$ (${\cal F}$ is a field invariant) are considered. It was shown that the metric function in both models possesses a de Sitter core without singularities as $r\rightarrow 0$. The behavior of the Hawking temperature and the heat capacity in these models are similar. The phase transitions take place when the Hawking temperature has a maximum, and black holes are thermodynamically stable at some event horizon radii when the heat capacity is positive. We show that the source of gravity in the Hayward model is questionable.