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The aim of this paper is to investigate the separability of a spin-1/2 spinorfield in a five-dimensional rotating, charged black hole constructed by Cveticand Youm in string theory, in the case when three U(1) charges are set equal.This black hole solution represents a natural generalization of the famousfour-dimensional Kerr-Newman solution to five dimensions with the inclusion ofa Chern-Simons term to the Maxwell equation. It is shown that the usual Diracequation can not be separated by variables in this general spacetime with twoindependent angular momenta. However if one supplements an additionalcounterterm into the usual Dirac operator, then the modified Dirac equation forthe spin-1/2 spinor particles is separable in this rotating, chargedEinstein-Maxwell-Chern-Simons black hole background geometry. A first-ordersymmetry operator that commutes with the modified Dirac operator has exactlythe same form as that previously found in the uncharged Myers-Perry black holecase. It is expressed in terms of a rank-three totally antisymmetric tensor andits covariant derivative. This tensor obeys a generalized Killing-Yano equationand its square is a second-order symmetric Stackel-Killing tensor admitted bythe five-dimensional rotating, charged black hole spacetime.Comment: 20 pages, accompanied paper to arXiv:0807.2114 [hep-th] and  arXiv:0808.3435 [hep-th]. Published versio

Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory