Scattering of scalar waves by rotating black holes

We study the scattering of massless scalar waves by a Kerr black hole by letting plane monochromatic waves impinge on the black hole. We calculate the relevant scattering phase-shifts using the Prufer phase-function method, which is computationally efficient and also reliable for high frequencies and/or large values of the angular multipole indices (l, m). We use the obtained phase-shifts and the partial-wave approach to determine differential cross sections and deflection functions. Results for off-axis scattering (waves incident along directions misaligned with the black hole's rotation axis) are obtained for the first time. Inspection of the off-axis deflection functions reveals the same scattering phenomena as in Schwarzschild scattering. In particular, the cross sections are dominated by the glory effect and the forward (Coulomb) divergence due to the long-range nature of the gravitational field. In the rotating case the overall diffraction pattern is `frame-dragged' and as a result the glory maximum is not observed in the exact backward direction. We discuss the physical reason for this behaviour, and explain it in terms of the distinction between prograde and retrograde motion in the Kerr gravitational field. Finally, we also discuss the possible influence of the so-called superradiance effect on the scattered waves.