Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations

We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal.