Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

We explore a formulation of thermodynamic geometry of black holes and prove that the divergent points of the specific heat correspond exactly to the singularities of the thermodynamic curvature. We investigate this correspondence for different types of black holes. This formulation can also be applied to an arbitrary thermodynamic system.Comment: 10 pages, 4 figures, typos fixed, references adde