Black Hole Thermodynamics in Carath\'eodory's Approach
  We show that, in the framework of Carath\'eodory's approach to thermodynamics, one can implement black hole thermodynamics by realizing that there exixts a quasi-homogeneity symmetry of the Pfaffian form $\deq$ representing the infinitesimal heat exchanged reversibly by a Kerr-Newman black hole; this allow us to calculate readily an integrating factor, and, as a consequence, a foliation of the thermodynamic manifold can be recovered. 
F.Belgiorno