Fast plunges into Kerr black holes

Abstract

Most extreme-mass-ratio-inspirals of small compact objects into supermassive black holes end with a fast plunge from an eccentric last stable orbit. For rapidly rotating black holes such fast plunges may be studied in the context of the Kerr/CFT correspondence because they occur in the near-horizon region where dynamics are governed by the infinite dimensional conformal symmetry. In this paper we use conformal transformations to analytically solve for the radiation emitted from fast plunges into near-extreme Kerr black holes. We find perfect agreement between the gravity and CFT computations.

Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms

“…We found that little changes in the fluxes during the plunge (i.e., where nonadiabatic effects are the largest) do not affect the waveform to any significant extent, because below the ISCO the motion is well approximated by a geodesic. So we expect that including nonadiabatic effects in the energy flux is not going to affect our (3,3), (3,2), (4,4), and (5,5) modes. The plots are for spin q ¼ 0.9.…”

“…4 It is relatively straightforward to estimate this discretization error: We first compute the waveforms at multiple grid resolutions, in particular we choose ðdr à ;dθÞ¼ðM=80;π=128Þ;ðM=40;π=64Þ and ðM=20; π=32Þ. Second, we derive the Richardson extrapolant using this data.…”

“…A vertical line marks the position of the peak of the orbital frequency, at time t Ω peak , which occurs close to merger. 4 Note that representing the singular particle-source terms using a narrow Gaussian distribution or a discrete delta [38,39] is potentially an additional source of error. However, that error is included in our measured discretization error, because that approximation is dependent on the discretization scale itself.…”

“…References [1][2][3][4] pointed out the possibility of describing analytically various processes of the dynamics and radiation in the near-horizon region of a nearly extremal black hole by exploiting an infinite-dimensional conformal symmetry that the Kerr metric satisfies in this particular limit. Applying the WKB method to the Teukolsky equation in the eikonal approximation, Ref.…”

“…In Sec. V we carry out a detailed study to understand and model the mixing of QNMs for the dominant (2,2), (2,1), (3,3), (3,2), (4,4), and (5,5) waveforms. In Sec.…”