Elastic scattering of waves by a black hole

The properties of a Schwarzschild black hole as an elastic scatterer of waves are studied in detail. Phase shifts and elastic scattering cross sections are obtained for a wide range of energy and angular momentum from the exact analytical solutions of the wave equation by employing computational techniques developed by the author in an earlier paper. Features of the low-frequency elastic scattering are pointed out, and comparison with other approximations is made. The angular distribution of the scattered waves is obtained for different values of the frequency. As could be expected, it presents a peak ($\propto {\theta }^{-4\mathrm{}}$) in the forward direction and a "glory" in the backward direction. For intermediate angles it shows a complicated oscillatory behavior as frequency increases that disappears only at the geometrical-optics limit. By using the elastic scattering parameters obtained here, we calculate the angular distribution of the absorbed waves. The differential absorption cross section is isotropic for low frequencies and gradually shows features of a diffraction pattern as frequency increases. It shows an absolute maximum in the forward direction which grows and narrows with the frequency. In the geometrical-optics limit there results a Dirac $\delta$ function.