HAMILTONIAN-FORMALISM FOR THE OPPENHEIMER-SNYDER MODEL - ART. NO. 064013

An effective action in Hamiltonian form is derived for a self-gravitat ing sphere of isotropic homogeneous dust. Starting from the Einstein-H ilbert action for baryotropic perfect fluids and making use of the sym metry and equation of state of the matter distribution we obtain a fam ily of reduced actions for two canonical variables, namely, the radius of the sphere and its ADM energy, the latter being conserved along tr ajectories of the former. These actions differ by the value of the (co nserved) geodesic energy of the radius of the sphere which defines (di sconnected) classes of solutions in correspondence to the inner geomet ry and proper volume of the sphere. By replacing the (fixed) geodesic energy with its expression in terms of the Schwarzschild time at the s urface of the sphere and treating the latter as a further canonical va riable we finally obtain an extended action which covers the full spac e of solutions. Generalization to the (inhomogeneous) Tolman model is shown to be straightforward. Quantization is also discussed. [S0556-28 21(98)02816-1].