Massless particle of any spin in static uncharged spherically symmetric curved spacetimes

Quantum equations for massless particles of any spin in static spherically symmetric spacetimes, namely, the Minkowski, FRW and Schwarzschild spacetimes are considered. The metrics of all three are diagonal and their corresponding E22 and E33 inverse veirbein fields are identical. Thus the angular wave functions are spherical harmonics spinors corresponding to simple modes specified by orbital angular momenta and their z component. By applying consistently a procedure based on variables separation it is shown that the radial wave functions are second order ordinary differential equations sharing the same homogeneous equation though nonhomogeneous terms are different depending on the characteristic E00 and E11 of each spacetime.