Analytic solutions of the Wheeler-DeWitt equation in spherically symmetric space-time

The canonical quantum theory of Einstein gravity with a cosmological constant in spherically symmetric space-time is analyzed. A mass operator can be introduced as a dynamical variable due to spherically symmetry. The operator ordering in the Hamiltonian, the momentum, and the mass operator is properly fixed so that they form a closed algebra. In this scheme, we obtain the analytic solution which simultaneously satisfies the Wheeler-DeWitt equation, the momentum constraint, and the mass constraint. [S0556-2821 (99)00312-4].