Initial data for stationary spacetimes near spacelike infinity

Abstract

We study Cauchy initial data forasymptotically flat, stationary vacuumspacetimes near spacelike infinity. Thefall-off behaviour of the intrinsic metricand the extrinsic curvature ischaracterized. We prove that they have ananalytic expansion in powers of a radialcoordinate. The coefficients of theexpansion are analytic functions of theangles. This result allow us to fill a gapin the proof found in the literature of thestatement that all asymptotically flat,vacuum stationary spacetimes admit ananalytic compactification at null infinity.Stationary initial data are physicallyimportant and highly non-trivial examplesof a large class of data with similarregularity properties at spacelikeinfinity, namely, initial data for whichthe metric and the extrinsic curvaturehave asymptotic expansion in terms ofpowers of a radial coordinate. We isolatethe property of the stationary data whichis responsible for this kind of expansion.