Work

On the Existence of Toric ALE and ALF Gravitational Instantons

Year: 2026

Type: article

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 singularities. 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.

Source: Annales Henri Poincaré

DOI: 10.1007/s00023-026-01767-z

Authors: Hari K. Kunduri, James Lucietti

Institutions: McMaster University, Maxwell Institute for Mathematical Sciences, University of Edinburgh

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: McMaster University, Natural Sciences and Engineering Research Council of Canada, Division of Mathematical Sciences