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arXiv · 2306.14567

Gravitational instantons with $S^1$ symmetry

Steffen Aksteiner·Lars Andersson·Mattias Dahl·Gustav Nilsson·Walter Simon
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Abstract

Uniqueness results for asymptotically locally flat and asymptotically flat $S^1$-symmetric gravitational instantons are proved using a divergence identity of the type used in uniqueness proofs for static black holes, combined with results derived from the $G$-signature theorem. Our results include a proof of the $S^1$-symmetric version of the Euclidean Black Hole Uniqueness conjecture, a uniqueness result for the Taub-bolt family of instantons, as well as a proof that an ALF $S^1$-symmetric instanton with the topology of the Chen-Teo family of instantons is Hermitian.

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Steffen Aksteiner, Lars Andersson, Mattias Dahl, Gustav Nilsson, Walter Simon. 2023-06-26. Gravitational instantons with $S^1$ symmetry. https://arxiv.org/abs/2306.14567

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