Abstract
In this paper, the consequences of the existence of a Killing–Yano tensor for the separability of the general relativistic Dirac equation in an exterior electromagnetic field are investigated. Those properties of Killing–Yano tensors, which are relevant for the subject of this work, are reviewed; it is then shown that for any class of metrics admitting this type of tensor the Dirac equation can be separated at least once. Furthermore, all separable systems which are obtained in this way are stated explicitly. Finally, for the special case of the Kerr solution, the formalism of the present paper is compared with Chandrasekhar’s work on the separability of the Dirac equation.
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