Taub-NUT as Bertrand spacetime with magnetic fields

Abstract

Based on symmetries Taub-NUT shares with Bertrand spacetime, we cast it as the latter with magnetic fields. Its nature as a Bianchi-IX gravitational instanton and other related geometrical properties are reviewed. We provide an easy derivation and comparison between the spatial Killing-Yano tensors deduced from first-integrals and the corresponding hyperk\"ahler structures and finally verify the existence of a graded Lie-algebra structure via Schouten-Nijenhuis brackets.