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Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-time

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Using the positive mass theorem, we show that the connectivity assumption of the black hole boundary is not necessary for proving the spherical symmetry of asymptotically Euclidean static vacuum space-time; thus there exist no asymptotically Euclidean static vacuum space-times with multiple black holes.

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Bunting, G.L., Masood-ul-Alam, A.K.M. Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-time. Gen Relat Gravit 19, 147–154 (1987).

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