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We study the separability of the Dirac equation for the four-dimensional STUblack hole space-time. In particular, we analyze in detail the separabilityconditions in the pair-wise equal charge STU black hole space-time\cite{Cvetic_PRD96}. While in the latter case the minimally coupled Diracequation is not separable the introduction of a specific torsion term ensuresthe separability. The source of the torsion is the Kalb-Ramond field, which isan integral part of String Theory, but further aspects of its properties andcoupling to fermionic fields remain to be studied. To derive the torsion twodifferent approaches are used in conformally related frames, showing that thetorsion is not unique. The correspondingly modified Dirac equations in theEinstein and String frames are shown to be separable. Furthermore, the masslessradial and angular wave-equations are examined, they show close similarity withcorresponding equations for the standard Kerr background. A generalization ofthe Teukolsky equation for the pair-wise equal case is conjectured. We alsobriefly analyze a technically sophisticated radial equation in the massivecase.

Separability of Dirac equation in the STU black hole space-time: pairwise-equal charge case study