On the existence of toric ALE and ALF gravitational instantons
Hari K. Kunduri, James Lucietti
TLDR
This paper proves existence and uniqueness for toric ALE/ALF gravitational instantons and shows self-dual ones are multi-Eguchi-Hanson/Taub-NUT.
Key contributions
- Establishes existence and uniqueness for asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) gravitational instantons.
- Proves unique, Ricci-flat, toric ALE/ALF instantons exist for every admissible rod structure, smooth up to conical singularities.
- Demonstrates that any toric ALE/ALF self-dual instanton is a multi-Eguchi-Hanson or multi-Taub-NUT solution.
Why it matters
This paper provides fundamental existence and uniqueness results for important classes of gravitational instantons. It clarifies their structure, showing how self-dual toric instantons relate to known solutions. These findings are crucial for understanding spacetime geometry in general relativity.
Original 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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