Geometrothermodynamics of higher dimensional black holes
  We study the thermodynamics and geometrothermodynamics of different black hole configurations in more than four spacetime dimensions. We find the conditions under which second order phase transitions occur in higher-dimensional static Reissner-Nordstr\"om and stationary Kerr black holes. Our results indicate that the equilibrium manifold of all these black hole configurations is in general curved and that curvature singularities appear exactly at those places where second order phase transitions occur. 
Alessandro Bravetti, Davood Momeni, Ratbay Myrzakulov and Hernando   Quevedo
gr-qc math-ph math.MP