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Phys. Rev. D 62, 044025 (2000) [5 pages]

Spherically symmetric dust shell and the time problem in canonical relativity

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Petr Hájíček
Institute for Theoretical Physics, University of Berne, Sidlerstrasse 5, CH–3012 Berne, Switzerland

Jerzy Kijowski
Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
Department of Mathematical Methods in Physics, University of Warsaw, ul. Hoża 74, 00-682 Warsaw, Poland

Received 16 March 2000; published 24 July 2000

The dynamics of a self-gravitating spherical dust shell is analyzed within the Hamiltonian formulation. Given any time variable on the shell, a complete reduction with respect to the momentum constraints is obtained and the true degrees of freedom of the composed “matter + gravity” system are found. The transition between two such formulations, corresponding to two different time parametrizations, is described as a canonical transformation in the reduced phase space. Explicit formulas for such a transformation are given. Implications for quantum gravity are discussed.


©2000 The American Physical Society

URL: http://link.aps.org/abstract/PRD/v62/e044025
DOI: 10.1103/PhysRevD.62.044025
PACS: 04.60.Ds, 04.20.Fy

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