nLab
Killing-Yano tensor

Definition

On a (pseudo-)Riemannian manifold $(X,g)$ a Killing-Yano tensor is a differential form $\omega$ such that

$${\nabla }_{(\mu }{\omega }_{{\alpha }_0),{\alpha }_1,\cdots ,{\alpha }_n}=0,$$\nabla_{(\mu} \omega_{\alpha_0), \alpha_1, \cdots , \alpha_n} = 0 \,,

where $\nabla$ is the covariant derivative with respect to the Levi-Civita connection of $g$.

There is also a variant of conformal Killing-Yano tensors

(…)

Properties

Killing-Yano tensors serve as “square roots” of Killing tensor. In a spacetime with a Killing tensor $H$ the relativistic particle has an extra conserved quantity. If it refines to a Killing-Yano tensor then also the spinning particle or superparticle has an extra odd conserved quantity. If $H=g$ then this is an extra worldline supersymmetry.

Examples

The Kerr spacetime admits a conformal Killing-Yano tensor (…)

Related concepts

• Killing vector

• Killing spinor

• Killing tensor

References

For instance

• O. P. Santillan, Killing-Yano tensors and some applications (arXiv:1108.0149)

• Jacek Jezierski, Maciej Łukasik, Conformal Yano-Killing tensor for the Kerr metric and conserved quantities (arXiv:gr-qc/0510058)

• W. Dietz and R. Rüdiger, Space-Times Admitting Killing-Yano Tensors. I Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences Vol. 375, No. 1762 (Mar. 31, 1981), pp. 361 (JSTOR)