A note about late-time wave tails on a dynamical background

Published 17 Dec 2009 in gr-qc | (0912.3474v1)

Abstract: 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 \cite{gpp2} 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 $t^{{-(2\ell+3)}$} at timelike infinity. We show that in the case of the time-dependent background Price's law holds only for $\ell=0$ while for each $\ell\geq 1$ the tail decays as $t^{{-(2\ell+2)}$.}