Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-01-24
J.Math.Phys. 42 (2001) 2590-2610
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, RevTeX, no figures, revised version, typos corrected, accepted for publication in Journal of Mathematical Physics
Scientific paper
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on the shell. These conditions and the gravitational field equations which follow from an initial variational principle, are used for elimination of the gravitational degrees of freedom. The transformation of the variational formula for spherically-symmetric systems leads to two natural variants of the effective action. One of these variants describes the shell from a stationary interior observer's point of view, another from the exterior one. The conditions of isometry of the exterior and interior faces of the shell lead to the momentum and Hamiltonian constraints. The canonical equivalence of the mentioned systems is shown in the extended phase space. Some particular cases are considered.
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