Taub-NUT as Bertrand spacetime with magnetic fields
Sumanto Chanda, Partha Guha, Raju Roychowdhury
TL;DR
This paper reinterprets the Taub-NUT spacetime as a Bertrand spacetime with magnetic fields, exploring its geometrical properties, symmetries, and algebraic structures to deepen understanding of its gravitational instanton nature.
Contribution
It provides a novel perspective by casting Taub-NUT as Bertrand spacetime with magnetic fields and analyzes its geometrical and algebraic structures in detail.
Findings
Taub-NUT can be viewed as Bertrand spacetime with magnetic fields.
Existence of spatial Killing-Yano tensors linked to hyperkähler structures.
Verification of a graded Lie-algebra structure via Schouten-Nijenhuis brackets.
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.
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