A Proof of Uniqueness of the Taub-bolt Instanton

Abstract

We show that the Riemannian Schwarzschild and the ``Taub-bolt'' instanton solutions are the only spaces (M,g) such that 1) M is a 4-dimensional, simply connected manifold with a Riemannian, Ricci-flat C^2-metric g which admits (at least) a 1-parameter group of isometries H without isolated fixed points on M. 2) The quotient (M L)/H (where L is the set of fixed points of H) is an asymptotically flat manifold, and the length of the Killing field corresponding to H tends to a constant at infinity.

arXiv comment20 pages. LaTeX. Substantially extended and corrected

References in corpus (2)

• Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem
• Nuts have no hair

Cited by in corpus (3)

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