On the Asymptotics for the Vacuum Einstein Constraint Equations
By Justin Corvino, R. Schoen. 2003
298 citations recorded by the source corpus.
In this paper we prove density of asymptotically flat solutions with special asymptotics in general classes of solutions of the vacuum constraint equations. The first type of special asymptotic form we consider is called harmonic asymptotics. This generalizes in a natural way the conformally flat asymptotics for the K = 0 constraint equations. We show that solutions with harmonic asymptotics form a dense subset (in a suitable weighted Sobolev topology) of the full set of solutions. An important feature of this construction is that the approximation allows large changes in the angular momentum. The second density theorem we prove allows us to approximate asymptotically flat initial data on a three-manifold M for the vacuum Einstein field equation by solutions which agree with the original data inside a given domain, and are identical to that of a suitable Kerr slice (or identical to a member of some other admissible family of solutions) outside a large ball in a given end. The construction generalizes work in [C], where the time-symmetric (K = 0) case was studied.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/9299f614bdad773b8d9e8318473259d2f0caa670
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Citations in the corpus
- Black Hole Remnants and the Information Loss Paradox (2014, background): “This result has since been extended to the Kerr geometry in [266].”
- No dynamics in the extremal Kerr throat (2009, background): “While [34] gives no bounds on the size of K2, it is natural to suppose that K2 can be taken to lie far down the throat in any limit in which K1 is also pushed far down the throat.”
- Stability of Black Holes and Black Branes (2012, unknown): “Proof: The proof of this lemma follows from the (much more general) techniques and results in [4, 5], and also [6].”
- Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds (2007, methodology): “Within the context of the approach taken in this paper, one possible way to accomplish this would be to extend the results of Corvino-Schoen [11, 12] and Chruściel-Delay [9] on initial data deformations to the asymptotically hyperbolic setting.”
- The Global Nonlinear Stability of Minkowski Space for Self-gravitating Massive Fields (2015, unknown): “We observe that the existence of initial data sets satisfying the conditions above was established by Corvino and Schoen [15]; see also Chrusciel and Delay [14] and the recent”
- Lessons from the information paradox (2020, methodology): “The Corvino-Schoen theorem [71] provides a generalization for the case without spherical symmetry.”
- The Holographic Nature of Null Infinity (2020, background): “relators of the Bondi mass with other operators and there is no classical analogue of this quantity. The non-uniqueness of classical boundary data near spatial innity is well known in the literature [40] and a nice discussion of the contrast between the amount of information available classically an”
- Inconsistency of islands in theories with long-range gravity (2021, methodology): “This is guaranteed in the classical theory by the Birkhoff theorem and its generalization by Corvino and Schoen [48].”
- 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].”