Dirac Equation in Kerr-NUT-(A)dS Spacetimes: Intrinsic Characterization of Separability in All Dimensions
Cariglia, M.; Krtouš, P.; Kubizňák, D.
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.
type: | article |
journal: | Phys. Rev. D |
volume: | 84 |
pages: | 024008 |
year: | 2011 |
eprint: | arXiv:1104.4123 |
grants: | Exact solutions in higher dimensional and classical gravity, GAČR 202/08/0187; 2008-2011; hlavní řešitel: Jiří Podolský |