Nuts have no hair

Abstract

We show that the Riemannian Kerr solutions are the only Riemannian, Ricci-flat and asymptotically flat ${\mathrm{C}}^2$-metrics $g_{\mu \nu }$ on a 4-dimensional complete manifold $\mathcal{M}$ of topology ${\mathrm{R}}^2\times {\mathrm{S}}^2$ 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.

8 pages, Latex file, no figures

References in corpus (1)

• There is no $R^{3}X{S}^1$ vacuum gravitational instanton

Cited by in corpus (5)

• A new AF gravitational instanton
• Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. $n\ge 5$
• An alternative to the Simon tensor
• A Proof of Uniqueness of the Taub-bolt Instanton
• A spacetime characterization of the Kerr-NUT-(A)de Sitter and related metrics