Integrability versus separability for the multi-centre metrics (Q1420245)

The multi-center metrics are Euclidean solutions of the empty space Einstein equations with self-dual curvature. Examples are the Taub-NUT and Eguchi-Hanson metrics. The author determines multi-center metrics having an additional conserved quantity, quadratic in the momenta, and induced by a Killing-Stäckel tensor. The approach results in a discovery of a subclass of metrics which correspond to new classically integrable dynamical systems. Their properties are studied.