Stability of Reissner-Nordström black holes

Extending some previous work, we here consider the even-parity perturbations of the Reissner-Nordström family of black holes. Gauge-invariant functions of the gravitational and electromagnetic perturbations are defined in terms of the standard Regge-Wheeler expansion functions, and the coupled wave equations obeyed by these quantities are given. The wave equations are decoupled by a simple transformation, and the decoupled equations are shown to admit no unstable normal-mode solutions obeying the appropriate boundary conditions.