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

By P. Chruściel, E. Delay. 2003

215 citations recorded by the source corpus.

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, singularityfree, vacuum space-times which are stationary in a neighborhood of i; 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 I ; 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. ∗Partially supported by a Polish Research Committee grant 2 P03B 073 24; email piotr@ gargan.math.univ-tours.fr †Visiting Scientist. Permanent address: Departement de Mathematiques, Faculte des Sciences, Parc de Grandmont, F37200 Tours, France. ‡Partially supported by the ACI program of the French Ministry of Research; email delay@ gargan.math.univ-tours.fr

Subfields: Astronomy and Astrophysics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/52b5fed653889fb73e42fe1f15a22c364e63c854

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. András Vasy
2. P. Hintz
3. S. Hollands
4. R. Schoen
5. R. Wald
6. Justin Corvino
7. Igor Rodnianski
8. Hans Lindblad

In Geometry and Topology

1. Justin Corvino
2. P. Hintz
3. András Vasy
4. R. Schoen
5. S. Hollands
6. Hong-wei Xu
7. M. Li
8. Burkhard Wilking

In Mathematical Physics

1. S. Hollands
2. R. Wald
3. P. Hintz
4. Justin Corvino
5. András Vasy
6. R. Schoen
7. K. Fredenhagen
8. K. Rejzner

Citations in the corpus

• Stability of Black Holes and Black Branes (2012, background): “Proof: The proof of this lemma follows from the (much more general) techniques and results in [4, 5], and also [6].”
• The global non-linear stability of the Kerr-de Sitter family of black holes (2016, methodology): “Such localized gluing methods for the constraint equations were first introduced by Corvino [30] for time-symmetric data; this restriction was subsequently removed by Corvino–Schoen [31], and Chruściel–Delay generalized their analysis in [26].”
• On the Asymptotics for the Vacuum Einstein Constraint Equations (2003, methodology): “of this paper (with the exception of Section 3) were announced in the spring of 2000, and have been widely communicated to the mathematical GR community. In the meantime, P.T. Chru´sciel and E. Delay [CD] have obtained a version of these results as well. Their paper employs our basic techniques (and”