  We extend the formulation for perturbations of maximally symmetric black
holes in higher dimensions developed by the present authors in a previous paper
(hep-th/0305147) to a charged black hole background whose horizon is described
by an Einstein manifold. For charged black holes, perturbations of
electromagnetic fields are coupled to the vector and scalar modes of metric
perturbations non-trivially. We show that by taking appropriate combinations of
gauge-invariant variables for these perturbations, the perturbation equations
for the Einstein-Maxwell system are reduced to two decoupled second-order wave
equations describing the behaviour of the electromagnetic mode and the
gravitational mode, for any value of the cosmological constant. These wave
equations are transformed into Schr\"odinger-type ODEs through a Fourier
transformation with respect to time. Using these equations, we investigate the
stability of generalised black holes with charge. We also give explicit
expressions for the source terms of these master equations with application to
the emission problem of gravitational waves in mind.
