Perturbation of the de Sitter-Schwarzschild universe with massless fields

The de Sitter-Schwarzschild universe is perturbed with massless fields of spin s=0, 1/2, 1, and 2. The linearized perturbation equations, obtained by the use of the spin coefficients, are found to be separable and the radial parts that remain are seen to combine in one general equation. This radial equation is then transformed into a one-dimensional wave equation, and taking the electromagnetic case as an example it is shown that the one-dimensional wave equation gives the reflection coefficient which is the same as that given by the general radial equation.