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.
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Communicated by A. Jaffe
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Christodoulou, D., O'Murchadha, N. The boost problem in general relativity. Commun.Math. Phys. 80, 271–300 (1981). https://doi.org/10.1007/BF01213014
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DOI: https://doi.org/10.1007/BF01213014