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arXiv · 2101.06700

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

Finnian Gray·Tsuyoshi Houri·David Kubiznak·Yukinori Yasui
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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.

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Finnian Gray, Tsuyoshi Houri, David Kubiznak, Yukinori Yasui. 2021-01-17. Symmetry operators for the conformal wave equation in rotating black hole spacetimes. https://doi.org/10.1103/physrevd.104.084042

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