Abstract
The spin-$\frac{3}{2}$ perturbations of the Kerr-Newman black holes are analyzed by linearizing the field equations of O(2) extended supergravity with respect to the spin-$\frac{3}{2}$ fields. The equations governing the spin-$\frac{3}{2}$ fields in Kerr-Newman geometry are decoupled and separated. All solutions that cannot be brought to zero by the supersymmetry transformations are shown to satisfy the generalized $s=\ifmmode\pm\else\textpm\fi{}\frac{3}{2}$ Teukolsky equations. The stationary solutions of these equations are not regular and hence cannot provide a new "hair" for the black holes. This generalizes the previous results obtained for the uncharged rotating black holes. However, it is also pointed out that the particular case where the electric charge equals the mass must be excluded from the argument.
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