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

Article

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

Sergyeyev, A.; Krtouš, P.

Phys. Rev. D 77, 044033 (2008)

Abstract

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.

Institute authors

Krtouš, Pavel

Supported by

GACR 202/08/0187 — Exact solutions in higher dimensional and classical gravity
MSM0021620860 — Fyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech

BibTeX

@article{UTF60,
  author        = {Sergyeyev, A. and Krtouš, P.},
  title         = {{Complete Set of Commuting Symmetry Operators for Klein–Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes}},
  journal       = {Phys. Rev. D},
  volume        = {77},
  pages         = {044033},
  year          = {2008},
  eprint        = {0711.4623},
  archivePrefix = {arXiv},
}