Taub-NUT as Bertrand spacetime with magnetic fields
arXiv:1503.08183 · doi:10.7546/jgsp-41-2016-33-67
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 hyperkähler structures and finally verify the existence of a graded Lie-algebra structure via Schouten-Nijenhuis brackets.
35 pages, contents and reference section modified, presentation improved, version to appear in JGSP, 35 pages