Quantum mechanics of the Schwarzschild-de Sitter black hole

In the present paper, we apply the quantum general relativity theory to the Schwarzschild-de Sitter black hole. We start by writing down the super-Hamiltonian and supermomentum constraints for general, neutral, spherically symmetric, space-times, with a positive cosmological constant. Then we solve the constraints for the canonical moments and canonically quantize the space-time using Dirac's formalism for constrained systems. The resulting operatorial equations are exactly solved in the WKB approximation, giving rise;to a wave function. Finally, for a particular ansatz of the canonical variables, we compute the quantum mechanical density probability and show how it depends on the mass of the hole and on the cosmological constant. [S0556-2821(98)03214-7].