HAMILTONIAN SPACETIME DYNAMICS WITH A SPHERICAL NULL-DUST SHELL

We consider the Hamiltonian dynamics of spherically symmetric Einstein gravity with a thin null-dust shell, under boundary conditions that f ix the evolution of the spatial hypersurfaces at the two asymptoticall y flat infinities of a Kruskal-like manifold. The constraints are elim inated via a Kuchar-type canonical transformation and Hamiltonian redu ction. The reduced phase space <(Gamma)over tilde> consists of two dis connected copies of R-4, each associated with one direction of the she ll motion. The right-moving and left-moving test shell limits can be a ttached to the respective components of <(Gamma)over tilde> as smooth boundaries with topology R-3. Choosing the right-hand-side and left-ha nd-side masses as configuration variables provides a global canonical chart on each component of <(Gamma)over tilde>, and renders the Hamilt onian simple, but encodes the shell dynamics in the momenta in a convo luted way. Choosing the shell curvature radius and the ''interior'' ma ss as configuration variables renders the shell dynamics transparent i n an arbitrarily specifiable stationary gauge ''exterior'' to the shel l, but the resulting local canonical charts do not cover the three-dim ensional subset of <(Gamma)over tilde> that corresponds to a horizon-s traddling shell. When the evolution at the infinities is freed by intr oducing parametrization clocks, we find on the unreduced phase space a global canonical chart that completely decouples the physical degrees of freedom from the pure gauge degrees of freedom. Replacing one infi nity by a flat interior leads to analogous results, but with the reduc ed phase space R-2 boolean OR W-2. Th, utility of the results for quan tization is discussed. [S0556-2821(98)03504-8].