English

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 nn-body configurations for n>1n > 1, 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

R2 v1 2026-06-21T11:40:25.757Z