Nuts have no hair

We show that the Riemannian Kerr solutions are the only Riemannian, Ricci-flat and asymptotically flat ${\rm C}^{2}$-metrics $g_{μν}$ on a 4-dimensional complete manifold ${\cal M}$ of topology ${\rm R}^{2} \times {\rm S}^{2}$ which have (at least) a 1-parameter group of periodic isometries with only isolated fixed points ("nuts") and with orbits of bounded length at infinity.

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