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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.
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Müller zum Hagen, H.: The static two body problem, Proc. Cambridge Philos. Soc. 75
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Beig, R.: The static gravitational field near spatial infinity, Gen Relativity Gravitation 12
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Bunting, G. L. and Masood-ul-Alam, A. K. M.: Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-time, Gen. Relativity Gravitation 19
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Andersson, L., Beig, R., and Schmidt, B. G.: Static self-gravitating elastic bodies in Einstein gravity, Comm. Pure Appl. Math. 61
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Beig, R. and Schmidt, B. G.: Celestial mechanics of elastic bodies, Math. Z. 258
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