Scattering and absorption of gravitational plane waves by rotating black holes

TL;DR

This paper investigates how gravitational waves scatter and are absorbed by rotating black holes, revealing effects like polarization, helicity change, and scattering peaks, with implications for gravitational wave detection.

Contribution

The study provides the first detailed numerical catalog of gravitational wave scattering by Kerr black holes, including new approximations and analysis of polarization and helicity effects.

Findings

Rotation causes polarization-dependent scattering effects.

Helicity is not conserved and can be amplified by superradiance.

Distinct glory and spiral scattering peaks are observed and characterized.

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 $M\omega \le 4$ and rotation rates $a \le 0.999M$. 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 $a\omega$. 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 $a = 0.999M$ at $M\omega = 0.945$). 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.