Late-time dynamics of rapidly rotating black holes - art. no. 104021

We study the late-time behavior of a dynamically perturbed rapidly rotating black hole. Considering an extreme Kerr black hole, we show that the large number of virtually undamped quasinormal modes (that exist for nonzero val ues of the azimuthal eigenvalue m) combine in such a way that the field (as observed at infinity) oscillates with an amplitude that decays as 1/t at l ate times. This is. in clear contrast to the standard late time power-law f alloff familiar from studies of nonrotating black holes. This long-lived os cillating "tail" will, however, not be present for nonextreme (presumably m ore astrophysically relevant) black holes, for which we find that many quas inormal modes (individually excited to a very small amplitude) combine to g ive rise to an exponentially decaying field. At very late, times this slowl y damped quasinormal-mode signal gives way to the standard power-law tail ( corresponding to a mixture of multipoles depending on the initial data). Th ese results could have implications for the detection of gravitational-wave signals from rapidly spinning black holes, since the required theoretical templates need to be constructed from linear combinations of many modes. Ou r main results are obtained analytically, but we support the conclusions wi th numerical time evolutions of the Teukolsky equation. These time evolutio ns provide an interesting insight into the notion that the quasinormal mode s can be viewed as waves trapped in the spacetime. region outside the horiz on. They also suggest that a plausible mechanism for the behavior we observ e for extreme black holes is the presence of a "superradiance resonance cav ity" immediately outside the black hole.