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The variational principle for a spherical configuration consisting of a thinspherical dust shell in gravitational field is constructed. The principle isconsistent with the boundary-value problem of the corresponding Euler-Lagrangeequations, and leads to ``natural boundary conditions''. These conditions andthe field equations following from the variational principle are used forperforming of the reduction of this system. The equations of motion for theshell follow from the obtained reduced action. The transformation of thevariational formula for the reduced action leads to two natural variants of theeffective action. One of them describes the shell from a stationary interiorobserver's point of view, another from the exterior one. The conditions ofisometry of the exterior and interior faces of the shell lead to the momentumand Hamiltonian constraints.Comment: 16 pages, LaTe

The Variational Principle and Effective Action for a Spherical Dust Shell