language: en

[BUTP-98/]

Relation between the simple, guessed, and the complicated, derived, super-Hamiltonians for shell dynamics

P. Hajcek
Institute for Theoretical Physics University of Bern
Sidlerstrasse 5, CH-3012 Bern, Switzerland
March 1998

Abstract The Hamiltonian dynamics of spherically symmetric massive thin shells in the general relativity is considered. Two different constraint dynamical systems representing this dynamics have been described recently; the relation of these two systems is investigated. The symmetry groups of both systems are found. The systems are reduced to the presymplectic manifolds 1 and 2 , lest non-physical aspects like gauge fixings or embeddings in extended phase spaces hinder the argument. The following facts are shown. 1 is three- and 2 is five-dimensional; the description of the shell dynamics by 1 is incomplete so that some measurable properties of the shell cannot be predicted. 1 is locally equivalent to a subsystem of 2 and the corresponding local morphisms are not unique, due to the large symmetry group of 2 . The local equivalence explains why the same radial equation results from both systems; what is, however, the physical importance of just local, but not global equivalence of constraint dynamical systems remains unclear.