2002/06/03 by Fabio Scardigli, Scardigli, Fabio
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0206009
PhD Thesis, 59 pages, University of Bern, December 2001
arxiv created 2002/06/03 · arxiv updated 2009/11/30
This Thesis concerns a thin fluid shell embedded in its own gravitational field. The starting point is a work of Hajicek and Kijowski, where the hamiltonian formalism for shell(s) (with no symmetry) in Einstein gravity is developed. An open problem at the end of that paper is to show how the hamiltonian formalism defines a regular constrained system: the hamiltonian and the constraints must be differentiable functionals on the phase space, so that their Poisson Brackets are well defined objects. On the contrary, some constraints at the shell result to be non differentiable functionals on the phase space. This problem is tackled, in the present thesis, by following the reduction procedure suggested by Teitelboim and Henneaux: the singular constraints are solved and the solution is substituted back into the hamiltonian. The resulting hamiltonian is shown to lead to equivalent dynamics, without singular constraints. Besides, the final reduced system (hamiltonian plus canonical constraints) is shown to be fully differentiable on the reduced phase space.