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

TL;DR

This paper provides an intrinsic characterization of the separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes across all dimensions, linking hidden symmetries with commuting operators and separability.

Contribution

It explicitly constructs a complete set of mutually commuting first-order operators, including the Dirac operator, derived from the principal conformal Killing-Yano tensor, establishing the link between symmetry and separability.

Findings

Existence of a complete set of commuting operators for the Dirac equation.

Operators are generated from the principal conformal Killing-Yano tensor.

Separable solutions correspond to the general solution found by Oota and Yasui.

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.