New Metrics Admitting the Principal Killing-Yano Tensor

TL;DR

This paper introduces new classes of Lorentzian and other signature metrics with principal Killing-Yano tensors, expanding the known geometries beyond the Euclidean case and revealing a richer structure of spacetimes in various dimensions.

Contribution

It constructs novel off-shell metrics admitting principal tensors with null eigenvalues, challenging previous assumptions and broadening the understanding of such geometries.

Findings

Discovered new Lorentzian metrics with principal tensors having null eigenvalues.

Uncovered a richer structure of spacetimes admitting principal tensors in multiple dimensions.

Made observations on the Kerr-Schild ansatz related to these metrics.

Abstract

It is believed that in any number of dimensions the off-shell Kerr-NUT-(A)dS metric represents a unique geometry admitting the principal (rank 2, non-degenerate, closed conformal Killing-Yano) tensor. The original proof relied on the Euclidean signature and therein natural assumption that the eigenvalues of the principal tensor have gradients of spacelike character. In this paper we evade this common wisdom and construct new classes of Lorentzian (and other signature) off-shell metrics admitting the principal tensor with null eigenvalues, uncovering so a much richer structure of spacetimes with principal tensor in four and higher dimensions. A few observations regarding the Kerr-Schild ansatz are also made.