Master Equations for Perturbations of Generalised Static Black Holes with Charge in Higher Dimensions

We extend the formulation for perturbations of maximally symmetric blackholes in higher dimensions developed by the present authors in a previous paper(hep-th/0305147) to a charged black hole background whose horizon is describedby an Einstein manifold. For charged black holes, perturbations ofelectromagnetic fields are coupled to the vector and scalar modes of metricperturbations non-trivially. We show that by taking appropriate combinations ofgauge-invariant variables for these perturbations, the perturbation equationsfor the Einstein-Maxwell system are reduced to two decoupled second-order waveequations describing the behaviour of the electromagnetic mode and thegravitational mode, for any value of the cosmological constant. These waveequations are transformed into Schr\"odinger-type ODEs through a Fouriertransformation with respect to time. Using these equations, we investigate thestability of generalised black holes with charge. We also give explicitexpressions for the source terms of these master equations with application tothe emission problem of gravitational waves in mind.Comment: 46 pages in the PTP-TEX style including 7 figures. The published versio