Phase transitions in geometrothermodynamic model of charged generalized-NUT black holes

Modern cosmological models are constructed in the framework of thermodynamic approaches developed within a Van der Waals-Maxwell theory of the first-order phase transitions. In the present work we study a geometrothermodynamics of two-dimensional first-order phase transition with the distribution of relaxation times in a configuration space which describes a spacetime with Newman-Unti-Tamburino-like metric. We utilized the geometrothermodynamical approach to construct the model of a charged generalized-NUT black hole. We reveal following features of the black-hole phase transition: there are series of bifurcations of pitchfork type in dependences of the Gibbs free energy on the Hawking temperature, and although a scalar Berwald curvature of space changes sign in the phase transition, black-hole stability depends on sign of the curvature after the transition.