TY - JOUR

T1 - On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime

AU - Houri, Tsuyoshi

AU - Tanahashi, Norihiro

AU - Yasui, Yukinori

N1 - Publisher Copyright:
© 2019 IOP Publishing Ltd.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.1088/1361-6382/ab586d

DO - 10.1088/1361-6382/ab586d

M3 - Article

AN - SCOPUS:85078489615

SN - 0264-9381

VL - 37

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 1

M1 - 015011

ER -