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 \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 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 = 0.999 M 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 .