Dirac Equation in Kerr-NUT-(A)dS Spacetimes: Intrinsic Characterization of Separability in All Dimensions

Article

Dirac Equation in Kerr-NUT-(A)dS Spacetimes: Intrinsic Characterization of Separability in All Dimensions

Cariglia, M.; Krtouš, P.; Kubizňák, D.

Phys. Rev. D 84, 024008 (2011)

Abstract

We intrinsically characterize separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions. Namely, we explicitly demonstrate that in such spacetimes there exists a complete set of first-order mutually commuting operators, one of which is the Dirac operator, that allows for common eigenfunctions which can be found in a separated form and correspond precisely to the general solution of the Dirac equation found by Oota and Yasui [arXiv:0711.0078]. Since all the operators in the set can be generated from the principal conformal Killing-Yano tensor, this establishes the (up to now) missing link among the existence of hidden symmetry, presence of a complete set of commuting operators, and separability of the Dirac equation in these spacetimes.

Institute authors

Krtouš, Pavel

Supported by

GACR 202/08/0187 — Exact solutions in higher dimensional and classical gravity

BibTeX

@article{UTF436,
  author        = {Cariglia, M. and Krtouš, P. and Kubizňák, D.},
  title         = {{Dirac Equation in Kerr-NUT-(A)dS Spacetimes: Intrinsic Characterization of Separability in All Dimensions}},
  journal       = {Phys. Rev. D},
  volume        = {84},
  pages         = {024008},
  year          = {2011},
  doi           = {10.1103/PhysRevD.84.024008},
  eprint        = {1104.4123},
  archivePrefix = {arXiv},
}