Geometrodynamics of Schwarzschild Black Holes

The curvature coordinates $T,R$ of a Schwarz-schild spacetime are turned into canonical coordinates $T(r),\mathsf{R}(r)$ on the phase space of spherically symmetric black holes. The entire dynamical content of the Hamiltonian theory is reduced to the constraints requiring that the momenta $P_{T}®, P_{\sf R}®$vanish\mathrm{.}Whatremainsisaconjugatepairofcanonicalvariables$m$and$p$whosevaluesarethesameoneveryembedding\mathrm{.}Thecoordinate$m$ is the Schwarzschild mass, and the momentum $p$ the difference of parametrization times at right and left infinities. The Dirac constraint quantization in the new representation leads to the state functional $\Psi (m; T, {\sf R}] = \Psi (m)$ which describes an unchanging superposition of black holes with different masses. The new canonical variables may be employed in the study of collapsing matter systems.