Stability of charged rotating black holes in the eikonal approximation

The stability of the exterior Kerr-Newman spacetime to high-frequency perturbations is investigated. The complex frequencies associated with the oscillations of a charged rotating black hole are determined for the perturbation angular momentum parameters j=1. The results are extended to j1 for slowly rotating black holes. These modes indicate that the exterior Kerr-Newman geometry is stable in the eikonal approximation.