Killing-Yano tensors and Nambu tensors

TL;DR

This paper explores the relationship between Killing-Yano tensors and Nambu tensors, demonstrating that in flat space all Killing-Yano tensors are Nambu tensors, and examining specific metrics where these tensors generate higher-order Nambu tensors.

Contribution

It establishes conditions under which Killing-Yano tensors become Nambu tensors and provides explicit examples in curved spacetimes like Taub-NUT and Kerr-Newman metrics.

Findings

All Killing-Yano tensors in flat space are Nambu tensors.

Killing-Yano tensors of order two generate Nambu tensors of order three in certain curved spacetimes.

Explicit examples in Taub-NUT and Kerr-Newman metrics support the theoretical results.

Abstract

We present the conditions when a Killing-Yano tensor becomes a Nambu tensor. We have shown that in the flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT metric and Kerr-Newmann metric we found that a Killing-Yano tensor of order two generate a Nambu tensor of order three.