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

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dc.creatorSergyeyev, Artur
dc.creatorKrtous, Pavel
dc.date2007-11-29
dc.date2008-01-08
dc.date.accessioned2026-07-07T11:13:26Z
dc.date.available2026-07-07T11:13:26Z
dc.descriptionWe 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 arXiv:hep-th/0612029 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 arXiv:hep-th/0611245 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. In the semiclassical approximation we find that the separated solutions of the Hamilton-Jacobi equation for geodesic motion are also solutions for a set of Hamilton-Jacobi-type equations which correspond to the quadratic conserved quantities arising from the above Killing tensors.
dc.description6 pages, no figures; typos in eq.(6) fixed; one reference added
dc.identifierhttps://arxiv.org/abs/0711.4623
dc.identifierhttp://arxiv.org/abs/0711.4623
dc.identifierPhys.Rev.D77:044033,2008
dc.identifierdoi:10.1103/PhysRevD.77.044033
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/191718
dc.subjectHigh Energy Physics - Theory
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.titleComplete Set of Commuting Symmetry Operators for the Klein-Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes
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