We present covariant symmetry operators for the conformal wave equation in the (off-shell) Kerr–NUT–AdS spacetimes. These operators, that are constructed from the principal Killing–Yano tensor, its ‘symmetry descendants’, and the curvature tensor, guarantee separability of the conformal wave equation in these spacetimes. We next discuss how these operators give rise to a full set of conformally invariant mutually commuting operators for the conformally rescaled spacetimes and underlie the $R$-separability of the conformal wave equation therein. Finally, by employing the WKB approximation we derive the associated Hamilton–Jacobi equation with a scalar curvature potential term and show its separability in the Kerr–NUT–AdS spacetimes.

• Received 29 April 2021
• Accepted 13 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.084042