Hamiltonian formalism for black holes and quantization

Starting from the Lagrangian formulation of the Einstein equations for the vacuum static spherically symmetric metric, we develop a canonical formalism in the radial variable r that is timelike inside the Schwarzschild horizon. The Schwarzschild mass turns out to be represented by a canonical function that commutes with the r-Hamiltonian. We investigate the Wheeler-DeWitt quantization and give the general representation for the solution as superposition of eigenfunctions of the mass operator.