Dipole Perturbations of the Reissner-Nordstrom Solution: The Polar Case

TL;DR

This paper extends Chandrasekhar's formalism to analyze dipole (l=1) polar perturbations of the Reissner-Nordstrom black hole, deriving the perturbed metric and electromagnetic components.

Contribution

It generalizes existing perturbation formalism to include dipole perturbations, providing explicit calculations of metric and electromagnetic perturbations.

Findings

Derived explicit formulas for dipole perturbations

Extended the formalism to include l=1 modes

Facilitates further stability and perturbation analysis

Abstract

The formalism developed by Chandrasekhar for the linear polar perturbations of the Reissner-Nordstrom solution is generalized to include the case of dipole (l=1) perturbations. Then, the perturbed metric coefficients and components of the Maxwell tensor are computed.