A Kummer construction for gravitational instantons
Olivier Biquard, Vincent Minerbe
TL;DR
This paper presents a unified construction method for various gravitational instantons with specific asymptotic behaviors, including new examples of ALH Ricci flat metrics, enriching the understanding of these geometric structures.
Contribution
It introduces a simple, uniform construction for known and new gravitational instantons with ALF, ALG, or ALH asymptotics, expanding the catalog of Ricci flat metrics.
Findings
Constructed all known deformation classes of gravitational instantons with specified asymptotics.
Developed new ALH Ricci flat metrics asymptotic to a line times a flat 3-manifold.
Provided a unified framework for understanding gravitational instantons.
Abstract
We give a simple and uniform construction of essentially all known deformation classes of gravitational instantons with ALF, ALG or ALH asymptotics and nonzero injectivity radius. We also construct new ALH Ricci flat metrics asymptotic to the product of a real line with a flat 3-manifold.
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