On the topology of vacuum spacetimes

Details On the topology of vacuum spacetimes On the topology of vacuum spacetimes

2002-06-12

arxiv.org/abs/gr-qc/0206034v2

Annales Henri Poincare 4:369-383,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, v2 is a substantial revision of the previous version: superfluous condition removed from main theorem and applicatio

Scientific paper

We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary compact manifold to an asymptotically Euclidean solution of the constraints on R^n. For any compact manifold which does not admit a metric of positive scalar curvature, this provides for the existence of asymptotically flat vacuum spacetimes with no maximal slices. Our main theorem is a special case of a more general gluing construction for nondegenerate solutions of the vacuum constraint equations which have some restrictions on the mean curvature, but for which the mean curvature is not necessarily constant. This generalizes the construction [IMP] (gr-qc/0109045), which is restricted to constant mean curvature data.

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