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arXiv · 2604.15159

On the existence of toric ALE and ALF gravitational instantons

Hari K. Kunduri·James Lucietti
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Abstract

We establish existence and uniqueness results for asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) gravitational instantons. In particular, we prove the existence of a unique, Ricci-flat, toric ALE and ALF gravitational instanton, for every admissible rod structure, that is smooth up to possible conical singularites. We also give an elementary proof that any toric ALE or ALF self-dual instanton is a multi-Eguchi-Hanson or multi-Taub-NUT solution.

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BibTeXRIS

Hari K. Kunduri, James Lucietti. 2026-04-16. On the existence of toric ALE and ALF gravitational instantons. https://arxiv.org/abs/2604.15159

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