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Communications in Mathematical Physics

, Volume 57, Issue 1, pp 83–96 | Cite as

The existence of non-trivial asymptotically flat initial data for vacuum spacetimes

  • Murray Cantor
Article

Abstract

This paper demonstrates the existence of non-trivial solutions (g, k) to the constraint equations of the initial value formulation of the Einstein field equations over ℝ3 withg ij − δ ij ∼ |x|−1 as |x| → ∞. Using the conformal methods of Lichnerowicz and York, this problem is divided into two parts. First, using weighted Sobolev spaces it is shown the set of pairs (g, k) withg a conformal metric andk transverse-traceless with respect tog forms a smooth vector bundleP with infinite dimensional fiber. Second, it is shown that the elements of a large open set inP uniquely determine a solution to the scalar constraint equation with the appropriate growth at infinity, and thereby determine solution to the constraint equations.

Keywords

Neural Network Complex System Initial Data Nonlinear Dynamics Sobolev Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Murray Cantor
    • 1
  1. 1.Department of MathematicsDuke UniversityDurhamUSA

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