Quantum states and the statistical entropy of the charged black hole

We quantize the Reissner-Nordstrom black hole using an adaptation of Kuchars canonical decomposition of the Kruskal extension of the Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional Schrodinger equation in Gaussian time by coupling the gravitational field to a reference fluid or dust. The physical phase space of the theory is spanned by the mass M, the charge Q, the physical radius R, the dust proper time tau, and their canonical momenta. The exact solutions of the functional Schrodinger equation imply that the difference in the areas of the outer and inner horizons is quantized in integer units. This agrees in spirit, but not precisely, with Bekenstein's proposal on the discrete horizon area spectrum of black holes. We also compute the entropy in the microcanonical ensemble and show that the entropy of the Reissner-Nordstrom black hole is proportional to this quantized difference in horizon areas.