We study scalar field and electromagnetic perturbations on Locally
Rotationally Symmetric (LRS) class II spacetimes, exploiting a recently
developed covariant and gauge-invariant perturbation formalism. From the
Klein-Gordon equation and Maxwell's equations, respectively, we derive
covariant and gauge-invariant wave equations for the perturbation variables and
thereby find the generalised Regge-Wheeler equations for these LRS class II
spacetime perturbations. As illustrative examples, the results are discussed in
detail for the Schwarzschild and Vaidya spacetime, and briefly for some classes
of dust Universes.Comment: 22 pages; v3 has minor changes to match published versio