Stefan-Boltzmann law for black bodies and black holes

Since black holes radiate with a thermal spectrum and therefore possess a radiation pressure, Boltzmann's derivation of Stefan's Law can be applied to black holes. In order that the entropy be proportional to the surface area of the black hole, the pressure must be negative. If the second law is not to be violated, then the temperature must also be negative. This leads to a canonical formulation for fluctuations. A comparison with other approaches is given and doubts are raised concerning the validity of conventional black hole thermodynamics.