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Complete Set of Commuting Symmetry Operators for Klein–Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes

Sergyeyev, A.; Krtouš, P.

We consider the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetime without imposing any restrictions on the functional parameters characterizing the metric. We establish commutativity of the second-order operators constructed from the Killing tensors found in [J. High Energy Phys. 02 (2007) 004] and show that these operators, along with the first-order operators originating from the Killing vectors, form a complete set of commuting symmetry operators (i.e., integrals of motion) for the Klein-Gordon equation. Moreover, we demonstrate that the separated solutions of the Klein-Gordon equation obtained in [J. High Energy Phys. 02 (2007) 005] are joint eigenfunctions for all of these operators. We also present explicit form of the zero mode for the Klein-Gordon equation with zero mass.
typ:article
journal:Phys. Rev. D
volume:77
pages:044033
year:2008
eprint:arXiv:0711.4623
odkaz:
files:
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