Einstein equations and Lagrangians on symmetry-restricted phase spaces

Details Einstein equations and Lagrangians on symmetry-restricted phase spaces Einstein equations and Lagrangians on symmetry-restricted phase spaces

Nov 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985gregr..17.1017f&link_type=abstract

General Relativity and Gravitation (ISSN 0001-7701), vol. 17, Nov. 1985, p. 1017-1024.

Physics

1

Cosmology, Einstein Equations, Euler-Lagrange Equation, Relativity, Big Bang Cosmology, Hilbert Space, Phase-Space Integral, Schwarzschild Metric, Symmetry

Scientific paper

When Lagrangians are restricted to subspaces of the phase space satisfying certain symmetry conditions, they do not always yield the correct Einstein equations. An example was found by Hawking (1969) in the Lagrangian for spatially homogeneous universes. First, it is shown that this problem is not limited to general relativity. Then, certain terms which do not appear in Lagrangians on symmetry-restricted phase spaces, but which nevertheless contribute to the Euler-Lagrange derivatives, are visualized. This general formula is applied to the Schwarzschild metric, the Friedmann universes, and spatially homogeneous universes.

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