On toric Hermitian ALF gravitational instantons
arXiv:2112.12711 · doi:10.1007/s00220-022-04562-z
Abstract
We give a classification of toric, Hermitian, Ricci flat, ALF Riemannian metrics in dimension 4, including metrics with conical singularities. The only smooth examples are on one hand the hyperKaehler ALF metrics, on the other hand, the Kerr, Taub-NUT and Chen-Teo metrics. There are examples with conical singularities with infinitely many distinct topologies. We provide explicit formulas.
A correct proof that the piecewise linear function is convex is written in the new section 4.5. Various minor corrections/typos