Phase transitions and geometrothermodynamics of regular black holes

In this paper we study the thermodynamics and state space geometry of a set of regular black hole solutions such as Bardeen black hole (1968), Ayón-Beato and García black hole (Phys Rev Lett 80:5056, 1998), Hayward black hole (Phys Rev Lett 96:031103, 2006) and Berej–Matyjasek–Trynieki–Wornowicz black hole (Gen Relativ Gravit 38(5):885906, 2006). We find that all these black holes show second order thermodynamic phase transitions by observing discontinuities in heat capacity–entropy graphs as well as the cusp type double point in free energy–temperature graph. Using the formulation of geometrothermodynamics we again find the singularities in the heat capacity of the black holes by calculating the curvature scalar of the Legendre invariant metric.