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.
type: | article |
journal: | Phys. Rev. D |
volume: | 77 |
pages: | 044033 |
year: | 2008 |
eprint: | arXiv:0711.4623 |
grants: | Exact solutions in higher dimensional and classical gravity, GAČR 202/08/0187; 2008-2011; hlavní řešitel: Jiří PodolskýFyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech, výzkumný záměr MSM0021620860; 2007-2013; hlavní řešitel: Jiří Bičák |