Late-time dynamics of rapidly rotating black holes

TL;DR

The paper investigates the late-time behavior of rapidly rotating black holes, revealing a 1/t decay of oscillations for extreme Kerr black holes due to undamped quasinormal modes, contrasting with exponential decay in non-extreme cases.

Contribution

It analytically and numerically demonstrates the distinct late-time decay patterns of perturbations in extreme versus non-extreme Kerr black holes, highlighting the role of quasinormal modes and superradiance.

Findings

Extreme Kerr black holes exhibit a 1/t decay of oscillations at late times.

Non-extreme black holes show exponential decay of perturbations.

The presence of a superradiance resonance cavity influences the decay behavior.

Abstract

We study the late-time behaviour 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 with the standard late time power-law fall-off familiar from studies of non-rotating black holes. This long-lived oscillating ``tail'' will, however, not be present for non-extreme (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. This result 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 behaviour we observe for extreme black holes is the presence of a ``superradiance resonance cavity'' immediately outside the black hole.