Scattering ofscalar waves by rotating black holes

Abstract

We study the scattering of massless scalar waves by a Kerr black hole byletting plane monochromatic waves impinge on the black hole. Wecalculate the relevant scattering phase-shifts using the Prüferphase-function method, which is computationally efficient and also reliablefor high frequencies and/or large values of the angular multipoleindices (l, m). We use the obtained phase-shifts and the partial-waveapproach to determine differential cross sections and deflectionfunctions. Results for off-axis scattering (waves incident alongdirections misaligned with the black hole's rotation axis) are obtained forthe first time. Inspection of the off-axis deflection functions reveals thesame 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 gravitationalfield. In the rotating case the overall diffraction pattern is`frame-dragged' and as a result the glory maximum is not observed in theexact backward direction. We discuss the physical reason for thisbehaviour, and explain it in terms of the distinction between prograde andretrograde motion in the Kerr gravitational field. Finally, we also discussthe possible influence of the so-called superradiance effect on thescattered waves.