No abstract

We show that any asymptotically flat initial data for the Einstein field equations have a development which includes complete spacelike surfaces boosted relative to the initial surface. Furthermore, the asymptotic fall off is preserved along these boosted surfaces and there exists a global system of harmonic coordinates on such a development. We also extend former results on global solutions of the constraint equations. By virtue of this extension, the constraint and evolution parts of the problem fit together exactly. Several theorems are given which concern the behaviour in the large of general classes of linear and quasilinear differential systems. This paper contains in addition a systematic exposition of the functional spaces employed.

The Hamiltonian constraint ``G00 = 8πT00'' of general relativity is written as a quasilinear elliptic differential equation for the conformal factor of the metric of a three-dimensional spacelike manifold. It is shown that for ``almost every'' configuration of initial data on a compact manifold, with or without boundary, a solution exists. Dirichlet boundary conditions are assumed if the boundary is not empty. The solution is unique.

Type of publicationArticle (peer-reviewed)Link to publisher's version https://journals.aps.org/prl/abstract

No abstract