Hamiltonian Treatment of the Complete Vacuum Schwarzschild Geometry

The complete vacuum Schwarzschild geometry is considered in its Hamiltonian form. There exists no canonical transformation that will make the constraints linear in the momentum canonically conjugate to the new time label. Consequently, no classical field exists such that its quantization on a flat background will be equivalent to the quantization of this geometry. A particular slicing shows that there are no true dynamical degrees of freedom even inside the horizon.