  This is the third in a series of papers which considers first-order
gauge-invariant and covariant gravitational perturbations to locally
rotationally symmetric (LRS) class II space-times. In this paper we complete
our analysis of the first-order gravito-electromagnetic (GEM) system by showing
how to derive three decoupled equations governing the GEM scalar fields. One of
these is for the gravito-magnetic scalar, whereas another two arise from the
2-gradient of the gravito-electric scalar.
