Black holes have no superhair

The no-hair conjecture is proved for the uncharged black holes of supergravity theory. The equations governing the spin-$\frac{3}{2}$ field in the Kerr geometry are decoupled and separated. All solutions that cannot be brought to zero by supersymmetry transformations are shown to satisfy the Teukolsky equations for $s=\pm \frac{3}{2}$. Such solutions cannot furnish a new hair for the black hole.