Twistor theory of the Chen--Teo gravitational instanton

TL;DR

This paper explicitly constructs holomorphic vector bundles over twistor space corresponding to the Chen--Teo family of Ricci-flat, ALF gravitational instantons, revealing their simple rational patching matrices.

Contribution

It provides explicit constructions and characterizations of the holomorphic bundles for the Chen--Teo instantons, advancing understanding of their twistor geometry.

Findings

Constructed explicit patching matrices for Chen--Teo instantons

Identified simple rational form of the patching matrices

Connected Ricci-flat metrics to holomorphic vector bundles over twistor space

Abstract

Toric Ricci--flat metrics in dimension four correspond to certain holomorphic vector bundles over a twistor space. We construct these bundles explicitly, by exhibiting and characterising their patching matrices, for the five--parameter family of Riemannian ALF metrics constructed by Chen and Teo. The Chen--Teo family contains a two--parameter family of asymptotically flat gravitational instantons. The patching matrices for these instantons take a simple rational form.