2003/01/31 by Piotr T. Chrusciel, Erwann Delay · 3 citations
Physics and Astronomy · #gr-qc
published as Mem.Soc.Math.France 94 (2003) 1-103 · latex2e, now 87 pages, several style files; various typos corrected, treatment of weighted Hoelder spaces improved, to appear in Memoires de la Societe Mathematique de France
arxiv created 2003/07/11 · arxiv updated 2009/11/30
Generalising an analysis of Corvino and Schoen, we study surjectivity properties of the constraint map in general relativity in a large class of weighted Sobolev spaces. As a corollary we prove several perturbation, gluing, and extension results: we show existence of non-trivial, singularity-free, vacuum space-times which are stationary in a neighborhood of i0; for small perturbations of parity-covariant initial data sufficiently close to those for Minkowski space-time this leads to space-times with a smooth global Scri; we prove existence of initial data for many black holes which are exactly Kerr -- or exactly Schwarzschild -- both near infinity and near each of the connected components of the apparent horizon; under appropriate conditions we obtain existence of vacuum extensions of vacuum initial data across compact boundaries; we show that for generic metrics the deformations in the Isenberg-Mazzeo-Pollack gluings can be localised, so that the initial data on the connected sum manifold coincide with the original ones except for a small neighborhood of the gluing region; we prove existence of asymptotically flat solutions which are static or stationary up to r-m terms, for any fixed m, and with multipole moments freely prescribable within certain ranges.