On Static n-body Configurations in Relativity
General Relativity and Quantum Cosmology
2009-03-24 v2
Abstract
The static n-body problem of General Relativity states that there are, under a reasonable energy condition, no static -body configurations for , provided the configuration of the bodies satisfies a suitable separation condition. In this paper we solve this problem in the case that there exists a closed, noncompact, totally geodesic surface disjoint from the bodies. This covers the situation where the configuration has a reflection symmetry across a noncompact surface disjoint from the bodies.
Keywords
Cite
@article{arxiv.0811.1727,
title = {On Static n-body Configurations in Relativity},
author = {Robert Beig and Richard M. Schoen},
journal= {arXiv preprint arXiv:0811.1727},
year = {2009}
}
Comments
10 pages; result generalized to allow for more than one asymptotically flat end