REDUCED PHASE-SPACE FORMALISM FOR SPHERICALLY SYMMETRICAL GEOMETRY WITH A MASSIVE DUST SHELL

We perform a Hamiltonian reduction of spherically symmetric Einstein g ravity with a thin dust shell of positive rest mass. Three spatial top ologies are considered: Euclidean (R-3), Kruskal ((SXR)-X-2), and the spatial topology of a diametrically identified Kruskal (RP3\ {a point at infinity}). For the Kruskal and RP3 topologies the reduced phase sp ace is four dimensional, with one canonical pair associated with the s hell and the other with the geometry, the latter pair disappears if on e prescribes the value of the Schwarzschild mass at an asymptopia or a t a throat. For the Euclidean topology the reduced phase space is nece ssarily two dimensional, with only the canonical pair associated with the shell surviving. A time reparametrization on a two-dimensional pha se space is introduced and used to bring the shell Hamiltonians to a s impler (and known) form associated with the proper time of the shell. An alternative reparametrization yields a square-root Hamiltonian that generalizes the Hamiltonian of a test shell in Minkowski space with r espect to Minkowski time. Quantization is briefly discussed. The discr ete mass spectrum that characterizes natural minisuperspace quantizati ons of vacuum wormholes and RP3 geons appears to persist as the geomet rical part of the mass spectrum when the additional matter degree of f reedom is added. [S0556-2821(97)00724-8].