**Authors**: Sam R. Dolan

**Date**: 8 May 2008

**Abstract**: The scattering cross section for a long-wavelength planar gravitational wave impinging upon a rotating black hole is calculated, for the special case in which the direction of incidence is aligned with the rotation axis. We show that black hole rotation leads to a term in the cross section that is proportional to $a\omega$. Hence, contrary to some claims, co-rotating and counter-rotating helicities are scattered differently, and a partial polarization is induced in an unpolarized incident wave.

The scattering amplitudes are found via partial wave series. To compute the series, two ingredients are required: phase shifts and spin-weighted spheroidal harmonics. We show that the phase shifts may be found from low-frequency solutions of the radial Teukolsky equation derived by Mano, Suzuki and Takasugi. The spheroidal harmonics may be expanded in spherical harmonics; we present expansions accurate to second order in $a \omega$. The two ingredients are combined to give explicit expressions for the helicity-conserving and helicity-reversing amplitudes, valid in the long-wavelength limit.

0805.1236
(/preprints)

2008-05-12, 08:39
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*