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Initial Data Engineering

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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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Authors and Affiliations

  1. Dept. de Mathématiques, Université de Tours, 37041, Tours Codex 1, France

    Piotr T. Chruściel

  2. Department of Physics, University of Oregon, Eugene, OR, 97403, USA

    James Isenberg

  3. Mathematics Department, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA

    Daniel Pollack

Authors
  1. Piotr T. Chruściel
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  2. James Isenberg
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  3. Daniel Pollack
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Corresponding author

Correspondence to Piotr T. Chruściel.

Additional information

Communicated by G.W. Gibbons

Partially supported by a Polish Research Committee grant 2 P03B 073 24

Partially supported by the NSF under Grants PHY-0099373 and PHY-0354659

Partially supported by the NSF under Grant DMS-0305048 and the UW Royalty Research Fund

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Chruściel, P., Isenberg, J. & Pollack, D. Initial Data Engineering. Commun. Math. Phys. 257, 29–42 (2005). https://doi.org/10.1007/s00220-005-1345-2

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  • DOI: https://doi.org/10.1007/s00220-005-1345-2

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