Reduced phase space formalism for spherically symmetric geometry with a massive dust shell

We perform a Hamiltonian reduction of spherically symmetric Einstein gravity with a thin dust shell of positive rest mass. Three spatial topologies are considered: Euclidean (R3), Kruskal (S2 × R), and the spatial topology of a diametrically identified Kruskal (RP\{a point at infinity}). For the Kruskal and RP topologies the reduced phase space is four-dimensional, with one canonical pair associated with the shell and the other with the geometry; the latter pair disappears if one prescribes the value of the Schwarzschild mass at an asymptopia or at a throat. For the Euclidean topology the reduced phase space is necessarily two-dimensional, with only the canonical pair associated with the shell surviving. A time-reparametrization on a twodimensional phase space is introduced and used to bring the shell HamiltoElectronic address: [email protected] On leave of absence from Department of Physics, University of Helsinki. Electronic address: [email protected] . Address after September 1, 1997: Max-Planck-Institut für Gravitationsphysik, Schlaatzweg 1, D–14473 Potsdam, Germany. Electronic address: [email protected] 1 nians to a simpler (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 respect to Minkowski time. Prospects for quantization are briefly discussed. Pacs: 04.20.Fy, 04.40.Nr, 04.60.Kz, 04.70.Dy Typeset using REVTEX 2