A Proof of Uniqueness of the Taub-bolt Instanton

Details A Proof of Uniqueness of the Taub-bolt Instanton A Proof of Uniqueness of the Taub-bolt Instanton

1998-09-28

arxiv.org/abs/gr-qc/9809076v2

Journal of Geometry and Physics 32 (1999) 211-226

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages. LaTeX. Substantially extended and corrected

Scientific paper

10.1016/S0393-0440(99)00023-6

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.

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