RELATION BETWEEN THE GUESSED AND THE DERIVED SUPER-HAMILTONIANS FOR SPHERICALLY SYMMETRICAL SHELLS - ART. NO. 084005

The Hamiltonian dynamics of spherically symmetric massive thin shells in general relativity is studied. Two different constraint dynamical s ystems representing this dynamics have been described recently; the re lation between these two systems is investigated. The symmetry groups of both systems are found. New variables are used, which among other t hings simplify the complicated system a great deal. The systems are re duced to presymplectic manifolds Gamma(1) and Gamma(2), lest nonphysic al aspects such as gauge fixing or embedding in extended phase spaces complicate the line of reasoning. The following facts are shown. Gamma (1) is three and Gamma(2) is five dimensional: the description of the shell dynamics by Gamma(1) is incomplete so that some measurable prope rties of the shell cannot be predicted. Gamma(1) is locally equivalent to a subsystem of Gamma(2) and the corresponding local morphisms are not unique, due to the large symmetry group of Gamma(2). Some conseque nces for the recent extensions of quantum shell dynamics through the s ingularity are discussed. [S0556-2821(98)04518-4].