On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications

dc.creatorChrusciel, Piotr T.
dc.creatorDelay, Erwann
dc.date2003-01-21
dc.date2003-07-11
dc.date.accessioned2026-07-07T03:27:33Z
dc.date.available2026-07-07T03:27:33Z
dc.descriptionGeneralising 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 $i^0$; 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.
dc.descriptionlatex2e, 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
dc.identifierhttps://arxiv.org/abs/gr-qc/0301073
dc.identifierhttp://arxiv.org/abs/gr-qc/0301073
dc.identifierMem.Soc.Math.France 94 (2003) 1-103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/34472
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleOn mapping properties of the general relativistic constraints operator in weighted function spaces, with applications
dc.typetext

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