Adiabatic evolution of Hayward black hole

In this letter we use the Carathéodory's approach to thermodynamics, to construct the thermodynamic manifold of the Hayward black hole. The Pfaffian form representing the infinitesimal heat exchange reversibly is considered to be δQ_rev≡dr_s−F_Hdl, previously obtained by Molina & Villanueva [1], where r_s is the Schwarzschild radius, l is the Hayward's parameter responsible for the possible regularization of the Schwarzschild black hole, and F_H is the intensive variable called the Hayward's force. By solving the associated Cauchy problem, the adiabatic paths are confined to the non-extremal manifold, and therefore, the status of the second and third laws are preserved. Consequently, the extremal sub-manifold corresponds to the adiabatically disconnected boundary of the manifold. In addition, the merger of two extremal Hayward black holes is analyzed.