Thermodynamic Properties of Radiation near the Black-Hole Horizon

With the approach of statistical physics we derive the thermodynamic functions for the scalar radiation near the horizon of a Schwarzschild black hole. The state equations are obtained, which are different from that obtained from the special relativity by the equivalence principle. The thermodynamic equilibrium can be achieved only if where T is the (local) temperature and is the red-shift factor, as the box containing the radiation approaches the horizon. The spectral distribution equation and the displacement law are obtained, which differ from the Planck distribution and the Wien's displacement law. The results can be easily extended to the electromagnetic radiation.