1+1+2 electromagnetic perturbations on non-vacuum LRS class II spacetimes: decoupling scalar and 2-vector harmonic amplitudes

Abstract

We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and Barrett [1] to analyze electromagnetic (EM) perturbations on non-vacuum locally rotationally symmetric (LRS) class II spacetimes. Ultimately, we show how to derive six real decoupled equations governing the total of six EM scalar and 2-vector harmonic amplitudes. Four of these are new, and result from expanding the complex EM 2-vector which we defined in [2] in terms of EM 2-vector harmonic amplitudes. We are then able to show that there are four precise combinations of the amplitudes that decouple, two of these are polar perturbations whereas the remaining two are axial. The remaining two decoupled equations are the generalized Regge–Wheeler equations which were developed previously in [3], and these govern the two EM scalar harmonic amplitudes. However, our analysis generalizes this by including a full description and classification of energy–momentum sources, such as charges and currents.