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arXiv · 0811.1727

On Static n-body Configurations in Relativity

Robert Beig·Richard M. Schoen
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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.

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Robert Beig, Richard M. Schoen. 2009-03-08. On Static n-body Configurations in Relativity. https://doi.org/10.1088/0264-9381%2F26%2F7%2F075014

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