Phase space for the Einstein equations

Details Phase space for the Einstein equations Phase space for the Einstein equations

2004-02-16

arxiv.org/abs/gr-qc/0402070v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, 0 figures, LaTeX2e, submitted to Comm Analysis and Geometry

Scientific paper

A Hilbert manifold structure is described for the ADM phase space of asymptotically flat initial data $(g,\pi)$ with local $H^2\times H^1$ Sobolev regularity. Solutions of the constraint equations form a Hilbert submanifold. A regularized RT Hamiltonian is defined and smooth on the full phase space and generates the Einstein evolution for any lapse-shift asymptotic to a (time) translation at infinity. Critical points for the total (ADM) mass, considered as a function on the Hilbert manifold of constraint solutions, arise precisely at initial data generating stationary vacuum spacetimes.

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