Phase space for the Einstein equations

Abstract

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.

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

References in corpus (1)

• On the Asymptotics for the Vacuum Einstein Constraint Equations