Phase space for the Einstein equations

Robert Bartnik

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arXiv · gr-qc/0402070

Phase space for the Einstein equations

Robert Bartnik

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Abstract

A Hilbert manifold structure is described for the ADM phase space of asymptotically flat initial data $(g,π)$ 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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Robert Bartnik. 2004-02-16. Phase space for the Einstein equations. https://arxiv.org/abs/gr-qc/0402070

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