, Volume 51, Issue 2, pp 163-182

A symplectic structure on the set of Einstein metrics

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Abstract

A symplectic structure i.e. a symplectic form Γ on the set of all solutions of the Einstein equations on a given 4-dimensional manifold is defined. A degeneracy distribution of Γ is investigated and its connection with an action of the diffeomorphism group is established. A multiphase formulation of General Relativity is presented. A superphase space for General Relativity is proposed.

Communicated by J. Ehlers