On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications
| dc.creator | Chrusciel, Piotr T. | |
| dc.creator | Delay, Erwann | |
| dc.date | 2003-01-21 | |
| dc.date | 2003-07-11 | |
| dc.date.accessioned | 2026-07-07T03:27:33Z | |
| dc.date.available | 2026-07-07T03:27:33Z | |
| dc.description | 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 $i^0$; 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.description | 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 | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0301073 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0301073 | |
| dc.identifier | Mem.Soc.Math.France 94 (2003) 1-103 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/34472 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications | |
| dc.type | text |