The boost problem in general relativity

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.

Asymptotically Flat Initial Data¶with Prescribed Regularity at Infinity

“…[12], [15], [16], [17] and the reference given there) and in weighted Hölder spaces [13]. The existence of initial data with non trivial momentum and angular momentum and the role of conformal symmetries have been analysed in some detail in [9].…”

“…Theorem 2.8 (Weak Maximum Principle) Assume that L given by (17) satisfies conditions (18), (19) and (20).…”

On the Topology of Vacuum Spacetimes

“…[14], [17], [5], [9], [10], [7], [8], [1], rely on it. This method is most successful when dealing with CMC data because in this case the equations decouple.…”

A Geometric Invariant Characterising Initial Data for the Kerr–Newman Spacetime

“…non-trivial Killing vectors of this type [9,12]. Thus, ξ AA is the spinorial counterpart of a real Killing vector.…”

“…One then commutes covariant derivatives using commutators (1) and makes use of the decompositions of ∇ AA κ BC , ∇ AA ξ BB and S AA BB given by Eqs. (11), (12) and (13), respectively, to simplify.…”