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Gravitational instantons with $S^1$ symmetry

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arxiv 2306.14567 v3 pith:FXC2EMJJ submitted 2023-06-26 math.DG gr-qc

Steffen Aksteiner , Lars Andersson , Mattias Dahl , Gustav Nilsson , Walter Simon This is my paper · ORCID
classification math.DGgr-qc
keywords instantonsuniquenessresultssymmetricasymptoticallyblackfamilyflat
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Mass Lower Bounds for Asymptotically Locally Flat Manifolds

    math.DG 2025-09 conditional novelty 7.0 of 10

    For ALF 4-manifolds with an almost free circle symmetry and nonnegative scalar curvature, mass is nonnegative and at least (ℓ/16) times the degree of the asymptotic circle bundle; in the AF case, homology-trivial coor...

  2. New asymptotically flat gravitational instanton

    gr-qc 2026-05 unverdicted novelty 6.0 of 10

    An explicit two-parameter metric is constructed for a new asymptotically flat toric gravitational instanton, the n=3 member of the Li-Sun family, with topology CP^2#CP^2 minus S^1.

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