How pure is the tail of gravitational collapse?

Waves propagating in a curved spacetime develop tails. In particular, it is well established that the late-time dynamics of gravitational collapse is dominated by a power-law decaying tail of the form Mt −(2 l +3) , where M is the black-hole mass. It should be emphasized, however, that in a typical evolution scenario there is a considerable time window in which the signal is no longer dominated by the black-hole quasinormal modes, but the leading-order power-law tail has not yet taken over. Higher order terms may have a considerable contribution to the signal at these intermediate times. It is, therefore, of interest to analyze these higher order corrections to the leading-order power-law behavior. We show that the higher order contamination terms die off at late times as M 2 t −4 ln( t / M ) for spherical perturbations, and as M 2 t −(2 l +4) ln 2 ( t / M ) for non-spherical ( l ≠ 0) perturbations. These results imply that the leading-order power-law tail becomes 'pure' (namely, with less than 1% contamination) only at extremely late times of the order of 10 4 M .