Relativistic analogue of the D'Alembert principle of virtual displacements and the effective actions for the spherically-symmetric charged dust shell in General Relativity

Details Relativistic analogue of the D'Alembert principle of virtual displacements and the effective actions for the spherically-symmetric charged dust shell in General Relativity Relativistic analogue of the D'Alembert principle of virtual displacements and the effective actions for the spherically-symmetric charged dust shell in General Relativity

2010-11-03

arxiv.org/abs/1011.0814v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

A simple and direct derivation of the variational principle and effective actions for a spherical charged dust shell in general relativity is offered. It is based on the relativistic version of the D'Alembert principle of virtual displacements and leads to the effective actions for the shell, thus describing its dynamics in terms of internal or external fixed observers. Herewith, sides of the shell are considered independently, in the coordinates of the interior or exterior region of the shell. Canonical variables for a charged dust shell are built. It is shown that the conditions of isometry of the sides of the shell lead to the Hamiltonian constraint on these internal and external dynamical systems. Special cases of the "hollow" and "screening" shells are briefly considered, as well as a family of the concentric charged dust shells.

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