## Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-time.(English)Zbl 0615.53055

The authors prove that the exterior Schwarzschild solution is the only maximally extended static, vacuum, asymptotically euclidean (in a sense specified in the paper) space-time with regular compact black-hole boundary. The connectedness of the black-hole boundary has not been assumed a priori, but it is a consequence of this result. Thus for the given type of space-times multiple black holes do not exist. The Schoen- Yau-Witten positive mass theorem is an essential tool for the proof of this result.
Reviewer: Bernd Wegner

### MSC:

 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 83C75 Space-time singularities, cosmic censorship, etc.
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### References:

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