Master equations for perturbations of generalized static black holes with charge in higher dimensions

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  • 20 August 2003
Abstract
We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed in our previous paper 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 the 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 2nd-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 to Schroedinger-type ODEs by the Fourier transformation with respect to time. Using these equations, we discuss the stability of generalized black holes with charge. We also give explict expressions for the source terms of these master equations with applications to the emission problem of gravitational waves in mind.

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