Conformal Yano–Killing (CYK) tensors are natural generalizations of conformal covector fields to the case of higher-rank differential forms. They are often responsible for hidden symmetries. Several spacetimes possess CYK tensors: Minkowski (the components are quadratic polynomials), (anti)de Sitter (a natural construction), Kerr (type-D spacetime), Taub-NUT (they lead to new symmetric conformal Killing tensors). CYK tensors are useful in several situations:
– Geometric definition of the asymptotic flat spacetime: strong asymptotic flatness which guarantees well-defined total angular momentum;
– Conserved quantities: asymptotic gravitational charges;
– Quasi-local mass and "rotational energy" for the Kerr black hole;
– Symmetries of the Dirac operator;
– Symmetries of Maxwell equations.
Thus, these nice geometrical objects are well worth studying in detail.