Late-time dynamics of rapidly rotating black holes

Abstract

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 values 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 late times. This is in clear contrast to the standard late time power-law falloff familiar from studies of nonrotating black holes. This long-lived oscillating ``tail'' will, however, not be present for nonextreme (presumably more astrophysically relevant) black holes, for which we find that many quasinormal modes (individually excited to a very small amplitude) combine to give rise to an exponentially decaying field. At very late times this slowly damped quasinormal-mode signal gives way to the standard power-law tail (corresponding to a mixture of multipoles depending on the initial data). These 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. Our main results are obtained analytically, but we support the conclusions with numerical time evolutions of the Teukolsky equation. These time evolutions provide an interesting insight into the notion that the quasinormal modes can be viewed as waves trapped in the spacetime region outside the horizon. They also suggest that a plausible mechanism for the behavior we observe for extreme black holes is the presence of a ``superradiance resonance cavity'' immediately outside the black hole.