On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications
Jan, 2003Citations per year
Abstract: (arXiv)
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 : 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 terms, for any fixed , and with multipole moments freely prescribable within certain ranges.References(0)
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