New Metrics Admitting the Principal Killing-Yano Tensor

Understand

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.