Symmetry operators for the conformal wave equation in rotating black hole spacetimes

Abstract

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 mutually commuting operators for the conformally rescaled spacetimes and underlie the R-separability of the conformal wave equation therein. Then, by employing the WKB approximation to the 'α-modified conformal wave equation' we derive an associated Hamilton-Jacobi equation with a scalar curvature potential term and show its separability in the Kerr-NUT-AdS spacetimes.