Thermodynamics, geometrothermodynamics and critical behavior of   (2+1)-dimensional black holes
  In this paper, we study the properties of the (2+1)-dimensional black holes from the viewpoint of geometrothermodynamics. We show that the Legendre invariant metric of the (2+1)-dimensional black holes can produce correctly the behavior of the thermodynamic interaction and phase transition structure of the corresponding black hole configurations. We find that they are both curved and the curvature scalar gives the information about the phase transition point. 
YiWen Han, Gang Chen
gr-qc