Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-07-05
Class.Quant.Grav. 18 (2001) 4329-4338
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTeX 2e, no figures, 12 pages
Scientific paper
10.1088/0264-9381/18/20/312
We study Cauchy initial data for asymptotically flat, stationary vacuum space-times near space-like infinity. The fall-off behavior of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic expansion in powers of a radial coordinate. The coefficients of the expansion are analytic functions of the angles. This result allow us to fill a gap in the proof found in the literature of the statement that all asymptotically flat, vacuum stationary space-times admit an analytic compactification at null infinity. Stationary initial data are physical important and highly non-trivial examples of a large class of data with similar regularity properties at space-like infinity, namely, initial data for which the metric and the extrinsic curvature have asymptotic expansion in terms of powers of a radial coordinate. We isolate the property of the stationary data which is responsible for this kind of expansion.
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