Electron in higher-dimensional weakly charged rotating black hole spacetimes

TL;DR

This paper proves the separability of the Dirac equation in higher-dimensional weakly charged rotating black hole spacetimes, revealing deep symmetry structures related to Killing-Yano tensors.

Contribution

It generalizes the integrability and separability results to charged fermions in higher dimensions, using symmetry operators derived from the principal Killing-Yano tensor.

Findings

Separable Dirac equation in higher-dimensional black holes

Symmetry operators generated by Killing-Yano tensors

Extension of charged particle integrability results

Abstract

We demonstrate separability of the Dirac equation in weakly charged rotating black hole spacetimes in all dimensions. The electromagnetic field of the black hole is described by a test field approximation, with vector potential proportional to the primary Killing vector field. It is shown that the demonstrated separability can be intrinsically characterized by the existence of a complete set of mutually commuting first order symmetry operators generated from the principal Killing-Yano tensor. The presented results generalize the results on integrability of charged particle motion and separability of charged scalar field studied in [1].