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=\ensuremath{\Vert}m\ensuremath{\Vert}\ensuremath{\gg}1. The results are extended to j\ensuremath{\ge}\ensuremath{\Vert}m\ensuremath{\Vert}\ensuremath{\gg}1 for slowly rotating black holes. These modes indicate that the exterior Kerr-Newman geometry is stable in the eikonal approximation.

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