Gravitational instantons with S¹ symmetry

2023/06/26 by Aksteiner, Steffen, Andersson, Lars, Dahl, Mattias +2 · 3 citations
#53C25 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2306.14567

Abstract

Uniqueness results for asymptotically locally flat and asymptotically flat S¹-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 S¹-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 S¹-symmetric instanton with the topology of the Chen-Teo family of instantons is Hermitian.

Cited by

• All toric Hermitian ALE gravitational instantons
• Mass Lower Bounds for Asymptotically Locally Flat Manifolds
• On the Chen-Teo family of stationary asymptotically locally Minkowskian black holes

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