No more CKY two-forms in the NHEK

TL;DR

This paper demonstrates that the space of conformal Killing-Yano two-forms remains two-dimensional in the near-horizon limit of Kerr-NUT-AdS black holes, with implications for understanding symmetries in these spacetimes.

Contribution

It establishes that the conformal Killing-Yano two-forms do not increase in number in the near-horizon limit, and derives a general $p$-form equation applicable in arbitrary dimensions.

Findings

The dimension of conformal Killing-Yano two-forms remains two in the near-horizon limit.

The conformal Killing-Yano $p$-form equation is formulated as parallel transport in arbitrary backgrounds.

Abstract

We show that in the near-horizon limit of a Kerr-NUT-AdS black hole, the space of conformal Killing-Yano two-forms does not enhance and remains of dimension two. The same holds for an analogous polar limit in the case of extremal NUT charge. We also derive the conformal Killing-Yano $p$-form equation for any background in arbitrary dimension in the form of parallel transport.