We show that the Riemannian Kerr solutions are the only Riemannian, Ricci-flat and asymptotically flat C2-metrics gμν on a 4dimensional complete manifold M of topology R2×S2 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. ∗Present address: Institut für theoretische Physik der Univ. Wien, Bol...