Abstract
We demonstrate separability of conformally coupled scalar field equation in general (off-shell) Kerr-NUT-AdS 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 Plebanski-Demianski spacetime.
Highlights
The four-dimensional Kerr black hole geometry possesses many remarkable properties
We demonstrate separability of conformally coupled scalar field equations in general 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
Summary
The four-dimensional Kerr black hole geometry possesses many remarkable properties. Among these perhaps the most intriguing is the separability of various test field equations in the Kerr black hole background. Higher-dimensional Kerr—Newman-Unti-Tamburino (NUT)—anti–de Sitter (AdS) family of vacuum black holes [11,12,13] admits a hidden symmetry of the principal Killing-Yano tensor, a nondegenerate closed conformal Killing-Yano 2-form [14], which in its turn generates towers of explicit and hidden symmetries and implies separability of a number of test field equations in these backgrounds [15]. The general separability of the massive Hamilton-Jacobi and scalar field equations was demonstrated in [16], the Dirac equation was separated in [17], the massless and massive vector perturbations in [18,19], and the harmonic p-form equations in [20], see [21] for partial results on separability of gravitational perturbations All these separability results remain true in a more general class of spacetimes admitting the principal Killing-Yano tensor.
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