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Communications in Mathematical Physics

, Volume 253, Issue 3, pp 561–583 | Cite as

Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries

  • David Maxwell
Article

Abstract

We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method used by Isenberg for compact manifolds without boundary, suitably extended to accommodate semilinear boundary conditions and low regularity metrics. As a consequence of our results for manifolds with boundary, we also obtain improvements to the theory of the constraint equations on asymptotically Euclidean manifolds without boundary.

Keywords

Boundary Condition Neural Network Manifold Complex System Nonlinear Dynamics 
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 Berlin Heidelberg 2004

Authors and Affiliations

  • David Maxwell
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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