On the topology of vacuum spacetimes
Abstract
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.
Keywords
Cite
@article{arxiv.gr-qc/0206034,
title = {On the topology of vacuum spacetimes},
author = {James Isenberg and Rafe Mazzeo and Daniel Pollack},
journal= {arXiv preprint arXiv:gr-qc/0206034},
year = {2016}
}
Comments
14 pages, v2 is a substantial revision of the previous version: superfluous condition removed from main theorem and applications to the existence of spacetimes with no maximal Cauchy surfaces added