Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries

Details Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries

2003-07-29

arxiv.org/abs/gr-qc/0307117v3

Commun.Math.Phys. 253 (2004) 561-583

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, 1 figure, TeX, v3. Final version to appear in CMP. Exposition has been extensively tightened and the proof of Propos

Scientific paper

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.

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