Communications in Mathematical Physics

, Volume 257, Issue 1, pp 29–42 | Cite as

Initial Data Engineering

  • Piotr T. Chruściel
  • James Isenberg
  • Daniel Pollack
Article

Abstract

We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be constant near the gluing points, which was the case for previous such constructions. No global conditions on the initial data sets such as compactness, completeness, or asymptotic conditions are imposed. As an application, we prove existence of spatially compact, maximal globally hyperbolic, vacuum space-times without any closed constant mean curvature spacelike hypersurface.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Piotr T. Chruściel
    • 1
  • James Isenberg
    • 2
  • Daniel Pollack
    • 3
  1. 1.Dept. de MathématiquesUniversité de ToursTours Codex 1France
  2. 2.Department of PhysicsUniversity of OregonEugeneUSA
  3. 3.Mathematics DepartmentUniversity of WashingtonSeattleUSA

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