Note about late-time wave tails on a dynamical background

Consider a spherically symmetric spacetime generated by a self-gravitating massless scalar field phi and let psi be a test (nonspherical) massless scalar field propagating on this dynamical background. Gundlach, Price, and Pullin [Phys. Rev. D 49, 890 ( 1994).] computed numerically the late-time tails for different multipoles of the field psi and suggested that solutions with compactly supported initial data decay in accord with Price's law as t(-(2l+3)) at timelike infinity. We show that in the case of the time-dependent background dispersing to Minkowski spacetime Price's law holds only for l = 0 while for each l >= 1 the tail decays as t(-(2l+2)).