Gravitational instantons with $S^1$ symmetry

Author:

Steffen Aksteiner, Lars Andersson, Mattias Dahl, Gustav Nilsson, Walter Simon

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), General Relativity and Quantum Cosmology (gr-qc)

journal:

date:

2023-06-25 16:00:00

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.

PDF: Gravitational instantons with $S^1$ symmetry.pdf