Gravitational waves from a plunge into a nearly extremal Kerr black hole

Abstract

We study numerically in the time domain the linearized gravitational waves emitted from a plunge into a nearly extremal Kerr black hole by solving the inhomogeneous Teukolsky equation. We consider spinning black holes for which the specific spin angular momentum a/M = 1 − ǫ, and we consider values of ǫ ≥ 10 −6 . We find an effective transient behavior for the quasi-normal ringdown: the early phase of the quasi-normal ringdown is governed by a decay according to inverse time, with frequency equaling twice the black hole's horizon frequency. The smaller ǫ the later the transition from this transient inverse time decay to exponential decay. Such sources, if exist, may be interesting potential sources for terrestrial or space borne gravitational wave observatories.

Particle motion near high-spin black holes

“…gives rise to the symmetric field strength (B13) and preserves near-AdS 2 time-translations: 24 L H0 A = 0.…”

Repeated ringing of black holes: Quasinormal bursts from highly eccentric, extreme mass-ratio binaries

“…This conclusion is not unexpected, as the analysis in Ref. [13] suggests that the transient decay rate for such a field would be ∼ u −1 because of the excitation of many quasi-normal overtones. The asymptotic faster decay rate at late retarded times is due to the nearly-extreme nature of the central black hole: the asymptotic behavior is that of a sub-extreme black hole.…”

“…We note that the peculiar aspects of the gravitational waveform in nearly-extreme Kerr black holes [13,14] e.g., the QNM portion of the scalar or gravitational waveform amplitude decays as M/u for near extremal Kerr black holes due to the unusual "stacking" of QNM overtones -is closely related to the QNB waveform. Moreover, the transient behavior of radiation fields in nearlyextreme Kerr black holes [12] is closely related to the transient behavior found herein.…”

“…In addition to the next periapsis passage that makes the available time series for determination of the decay rate finite and short, we have an additional complication from the transient nature of nearly-extreme black holes. Specifically, even close to extremality eventually the nearly-extreme black hole behaves like sub-extreme ones [12,13]. The decay rate of the QNB amplitude deviates as a transient behavior from the exponential decay rate of a single QNM because of the many overtones that contribute to it.…”

“…We emphasize that while the inverse (retarded) time behavior of the amplitude is by no means a new phenomenon, and is closely related to the behavior found in Refs. [13][14][15], the time dependence of the frequency is new, to the plotted at I + as a function of retarded time u for the same orbital parameters as in Fig. 3, for a/M = 0.995, 0.999 9, 0.999 95, 0.999 99.…”