On Static n-body Configurations in Relativity

Abstract

The 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 end

References in corpus (5)

• Towards a classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
• The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
• Spherically symmetric relativistic stellar structures
• Static self-gravitating elastic bodies in Einstein gravity
• Celestial mechanics of elastic bodies

Cited by in corpus (14)

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• Non-existence of stationary two-black-hole configurations: The degenerate case
• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Binary black hole system at equilibrium
• Static potentials on asymptotically flat manifolds
• Rotating Electroweak Sphaleron-Antisphaleron Systems
• Gravitating Opposites Attract
• Brendle's inequality on static manifolds
• Static self-gravitating many-body systems in Einstein gravity
• Properties of Charged Rotating Electroweak Sphaleron-Antisphaleron Systems
• Self-gravitating elastic bodies
• Soliton methods and the black hole balance problem