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

TL;DR

This paper develops covariant symmetry operators for the conformal wave equation in Kerr-NUT-AdS spacetimes, enabling separability and integrability, and explores their implications for conformal invariance and the Hamilton-Jacobi equation.

Contribution

It introduces new symmetry operators based on the principal Killing-Yano tensor that ensure separability of the conformal wave equation in rotating black hole spacetimes.

Findings

Operators guarantee separability of the conformal wave equation.

Construction of mutually commuting conformally invariant operators.

Derivation and separability of the Hamilton-Jacobi equation with curvature potential.

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 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.