Rough Solutions of the Einstein Constraint Equations on Compact Manifolds

Details Rough Solutions of the Einstein Constraint Equations on Compact Manifolds Rough Solutions of the Einstein Constraint Equations on Compact Manifolds

2005-06-15

arxiv.org/abs/gr-qc/0506085v1

J.Hyperbol.Diff.Equat.2:521,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages, included in Miami Waves 2004 proceedings

Scientific paper

10.1142/S021989160500049X

We construct low regularity solutions of the vacuum Einstein constraint equations on compact manifolds. On 3-manifolds we obtain solutions with metrics in $H^s$ where $s>3/2$. The constant mean curvature (CMC) conformal method leads to a construction of all CMC initial data with this level of regularity. These results extend a construction from Ma04 that treated the asymptotically Euclidean case.

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