On toric Hermitian ALF gravitational instantons

Olivier Biquard (1) , Paul Gauduchon (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Domains: Differential Geometry [math.DG]

Olivier Biquard, Paul Gauduchon. On toric Hermitian ALF gravitational instantons. Communications in Mathematical Physics, 2023, 399, pp.389-422. ⟨10.1007/s00220-022-04562-z⟩. ⟨hal-03501981⟩