Scalar field and electromagnetic perturbations on locally rotationally symmetric spacetimes

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 generalized 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.