On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime

Abstract

We focus on the method recently proposed by Lunin and Frolov-Krtouš-Kubizňák to solve the Maxwell equation on the Kerr-NUT-(A)dS spacetime by separation of variables. In their method, it is crucial that the background spacetime has hidden symmetries because they generate commuting symmetry operators with which the separation of variables can be achieved. In this work we reproduce these commuting symmetry operators in a covariant fashion. We first review the procedure known as the Eisenhart-Duval lift to construct commuting symmetry operators for given equations of motion. Then we apply this procedure to the Lunin-Frolov-Krtouš-Kubizňák (LFKK) equation. It is shown that the commuting symmetry operators obtained for the LFKK equation coincide with the ones previously obtained by Frolov-Krtouš-Kubizňák, up to first-order symmetry operators corresponding to Killing vector fields. We also address the Teukolsky equation on the Kerr-NUT-(A)dS spacetime and its symmetry operator is constructed.

26 pages, 1 figure. v2: typos corrected

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Cited by in corpus (8)

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• Massive vector fields in Kerr--Newman and Kerr--Sen black hole spacetimes
• Separable electromagnetic perturbations of rotating black holes
• Rotating and charged Taub-NUT-(A)dS spacetimes on a 3-brane
• First Order Symmetry Operators for the Linearized Field Equation of Metric Perturbations
• Separation of variables in the WZW models
• Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes
• On First Order Symmetry Operators for the Field Equations of Differential Forms