  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.
