Non-existence of f-symbols in generalized Taub-NUT spacetimes
Ion I. Cot\u{a}escu, Mihai Visinescu
TL;DR
This paper proves that most generalized Taub-NUT spacetimes lack f-symbols, with the exception of the original Taub-NUT metric which uniquely admits four Killing-Yano tensors, highlighting limitations in their hidden symmetries.
Contribution
It extends previous work by showing that generalized Taub-NUT metrics generally do not admit f-symbols, except for the original Taub-NUT case.
Findings
Generalized Taub-NUT metrics lack f-symbols.
Original Taub-NUT admits four Killing-Yano tensors.
Most extensions do not have hidden symmetries.
Abstract
In a previous article it was proved that the extensions of the Taub-NUT geometry do not admit Killing-Yano tensors, even if they possess St\" {a}ckel-Killing tensors. Here the analysis is taken further, and it is shown that, in general, this class of metrics does not even admit f-symbols. The only exception is the original Taub-NUT metric which possesses four Killing-Yano tensors of valence two.
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