Quantum states and the statistical entropy of the charged black hole - art. no. 024008

We quantize the Reissner-Nordstrom black hole using an adaptation of Kuchar s canonical decomposition of the Kruskal extension of the Schwarzschild bla ck hole. The Wheeler-DeWitt equation turns into a functional Schrodinger eq uation 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 mas s M, the charge Q, the physical radius R, the dust proper time tau, and the ir canonical momenta. The exact solutions of the functional Schrodinger equ ation imply that the difference in the areas of the outer and inner horizon s is quantized in integer units. This agrees in spirit, but not precisely, with Bekenstein's proposal on the discrete horizon area spectrum of black h oles. We also compute the entropy in the microcanonical ensemble and show t hat the entropy of the Reissner-Nordstrom black hole is proportional to thi s quantized difference in horizon areas.