Dipole perturbations of the Reissner-Nordström solution. II. The axial case

We study the linear metric perturbations of the Reissner-Nordström solution for the case of axial perturbation modes. We find that the well-known perturbative analysis fails for the case of dipole $\mathrm{}(l=1\mathrm{})\mathrm{}$ perturbations, although valid for higher multipoles. We define new radial functions, with which the perturbation formalism is generalized to all multipole orders, including the dipole. We then complete the solution by constructing the perturbed metric and Maxwell tensors.