Geometric description of the thermodynamics of a black hole with power   Maxwell invariant source
  Considering a nonlinear charged black hole as a thermodynamics system, we study the geometric description of its phase transitions. Using the formalism of geometrothermodynamics we show that the geometry of the space of thermodynamic equilibrium states of this kind of black holes is related with information about thermodynamic interaction, critical points and phase transitions structure. Our results indicate that the equilibrium manifold of this black hole is curved and that curvature singularities appear exactly at those places where first and second order phase transitions occur. 
Gustavo Arciniega and Alberto S\'anchez
math-ph gr-qc math.MP