A superradiance resonance cavity outside rapidly rotating black holes

TL;DR

Analytical results for near-extreme Kerr black holes 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 oscillates with an amplitude that decays as 1/t at late times.

Abstract

We discuss the late-time behaviour of a dynamically perturbed Kerr black hole. We present analytic results for near extreme Kerr black holes that 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 oscillates with an amplitude that decays as 1/t at late times. This prediction is verified using numerical time-evolutions of the Teukolsky equation. We argue that the observed behaviour may be relevant for astrophysical black holes, and that it can be understood in terms of the presence of a ``superradiance resonance cavity'' immediately outside the black hole.

Figures (2)

• Figure 1: A numerical evolution showing the late-time behaviour of a scalar field in the geometry of a rapidly rotating black hole. We show the field as viewed by an observer situated well away from the black hole for $a=M$. At late times the field falls off according to an oscillating power-law with the amplitude decaying as $1/t$.
• Figure 2: Schematic explanation of the new phenomenon seen in the numerical evolutions of Kerr perturbations. The left panel illustrates the standard scenario: An infalling pulse excites the QNMs that then propagate to infinity and the horizon. At late times, backscattering due to the curvature in the far-zone dominates and leads to the familiar power-law tail behaviour. Right panel: Frequencies that lie in the superradiant regime experience a "potential peak" in the region $[r_+,\infty]$. Hence, there will be a superradiance resonance cavity outside the black hole. At late times, the waves leaking out of this cavity to infinity dominate the signal.