Conformally coupled scalar in rotating black hole spacetimes

We demonstrate separability of conformally coupled scalar field equations in general (off-shell) Kerr - Newman-Unti-Tamburino - anti-de Sitter spacetimes in all dimensions. The separability is intrinsically characterized by the existence of a complete set of mutually commuting conformal wave operators that can be constructed from a hidden symmetry of the principal Killing-Yano tensor. By token of conformal symmetry, the separability also works for any Weyl rescaled (off-shell) metrics. This is especially interesting in four dimensions where it guarantees separability of a conformally coupled scalar field in the general Plebański-Demiański spacetime.