Nuts Have No Hair

Research Report MRR95-052

Nuts Have No Hair

Walter Simon

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

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