2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224206The static n-body problem of General Relativity states that there are, under a reasonable energy condition, no static $n$-body configurations for $n > 1$, 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.10 pages; result generalized to allow for more than one asymptotically flat endGeneral Relativity and Quantum Cosmologytext