Scattering and absorption of gravitational plane waves by rotating black holes

Sam R. Dolan

doi:10.1088/0264-9381/25/23/235002

paper

Scattering and absorption of gravitational plane waves by rotating black holes

arXiv:0801.3805 · doi:10.1088/0264-9381/25/23/235002

Abstract

This is a study of the scattering and absorption of planar gravitational waves by a Kerr black hole in vacuum. We apply the partial wave method to compute cross sections for the special case of radiation incident along the rotation axis. A catalogue of numerically-accurate cross sections is presented, for a range of incident wavelengths $M ω \leq 4$ and rotation rates $a \leq 0.999 M$ . Three effects are studied in detail: polarization, helicity-reversal and glory scattering. First, a new approximation to the polarization in the long-wavelength limit is derived. We show that black hole rotation distinguishes between co- and counter-rotating wave helicities, leading to a term in the cross section proportional to $aω$ . Second, we confirm that helicity is not conserved by the scattering process, and show that superradiance amplifies the effect. For certain wavelengths, the back-scattered flux is enhanced by as much as $\sim 35$ times for a rapidly-rotating hole (e.g. for $a = 0.999 M$ at $M ω = 0.945$ ). Third, we observe regular glory and spiral scattering peaks in the numerically-determined cross sections. We show that the angular width and intensity of the peaks may be estimated via a semi-classical approximation. We conclude with a discussion of the observable implications of our results.

43 pages, 17 figures. To match published version

Scattering and absorption of gravitational plane waves by rotating black holes

Abstract

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