Construction of metric and vector potential perturbations of a Reissner–Nordström black hole

Abstract

When an appropriate decoupling of variables in a coupled linear system of partial differential equations is obtained, a recently described procedure enables one to construct solutions to the full coupled system of equations. We employ this procedure here to generate solutions of the linearized Einstein–Maxwell equations describing perturbations of a Reissner–Nordström black hole, using Chandrasekhar’s recent decoupling of these equations. Explicit formulae are given for the metric and vector potential perturbations for each parity type.