Abstract
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 , Kruskal , and the spatial topology of a diametrically identified Kruskal a point at infinity. For the Kruskal and 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 two-dimensional phase space is introduced and used to bring the shell Hamiltonians 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. Quantization is briefly discussed. The discrete mass spectrum that characterizes natural minisuperspace quantizations of vacuum wormholes and geons appears to persist as the geometrical part of the mass spectrum when the additional matter degree of freedom is added.
- Received 30 July 1997
DOI:https://doi.org/10.1103/PhysRevD.56.7674
©1997 American Physical Society