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The Einstein-Scalar Field Constraints on Asymptotically Euclidean Manifolds*

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Abstract

By using the conformal method, solutions of the Einstein-scalar field gravitational constraint equations are obtained. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz equation, rather than just one. The proofs are constructive and allow for arbitrary dimension (> 2) as well as low regularity initial data.

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Authors and Affiliations

  1. Academie des Sciences, 23 Quai Conti, 75270, Paris 06, France

    Yvonne Choquet-Bruhat

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

    James Isenberg

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

    Daniel Pollack

Authors
  1. Yvonne Choquet-Bruhat
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  2. James Isenberg
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  3. Daniel Pollack
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Corresponding author

Correspondence to Yvonne Choquet-Bruhat.

Additional information

Project supported by NSF Grant PHY-0354659 at the University of Oregon, and by NSF Grant DMS-0305048 at the University of Washington.

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Choquet-Bruhat, Y., Isenberg, J. & Pollack, D. The Einstein-Scalar Field Constraints on Asymptotically Euclidean Manifolds*. Chin. Ann. Math. Ser. B 27, 31–52 (2006). https://doi.org/10.1007/s11401-005-0280-z

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  • DOI: https://doi.org/10.1007/s11401-005-0280-z

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