Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-12-22
Class.Quant.Grav. 19 (2002) 2567-2586
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
26 pages, Latex file using amstex, some references corrected
Scientific paper
10.1088/0264-9381/19/10/304
The study of the two-shell system started in ``Pair of null gravitating shells I and II'' (gr-qc/0112060--061) is continued. The pull back of the Liouville form to the constraint surface, which contains complete information about the Poisson brackets of Dirac observables, is computed in the singular double-null Eddington-Finkelstein (DNEF) gauge. The resulting formula shows that the variables conjugate to the Schwarzschild masses of the intershell spacetimes are simple combinations of the values of the DNEF coordinates on these spacetimes at the shells. The formula is valid for any number of in- and out-going shells. After applying it to the two-shell system, the symplectic form is calculated for each component of the physical phase space; regular coordinates are found, defining it as a symplectic manifold. The symplectic transformation between the initial and final values of observables for the shell-crossing case is written down.
Hajicek Peter
Kouletsis Ioannis
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