Pair of null gravitating shells II. Canonical theory and embedding variables

Details Pair of null gravitating shells II. Canonical theory and embedding variables Pair of null gravitating shells II. Canonical theory and embedding variables

2001-12-22

arxiv.org/abs/gr-qc/0112061v2

Class.Quant.Grav. 19 (2002) 2551-2566

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, Latex file using amstex, some references corrected

Scientific paper

10.1088/0264-9381/19/10/303

The study of the two shell system started in our first paper ``Pair of null gravitating shells I'' (gr-qc/0112060) is continued. An action functional for a single shell due to Louko, Whiting and Friedman is generalized to give appropriate equations of motion for two and, in fact, any number of spherically symmetric null shells, including the cases when the shells intersect. In order to find the symplectic structure for the space of solutions described in paper I, the pull back to the constraint surface of the Liouville form determined by the action is transformed into new variables. They consist of Dirac observables, embeddings and embedding momenta (the so-called Kucha\v{r} decomposition). The calculation includes the integration of a set of coupled partial differential equations. A general method of solving the equations is worked out.

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