Absorption and emission spectra of a Schwarzschild black hole

The absorption spectrum of a Schwarzschild black hole is studied in detail. Accurate and useful computational methods based on the analytical resolution of the wave equation are developed. In this way phase shifts and absorption cross sections are obtained for a wide range of energy and angular momentum. Comparison with the explicit results valid for low and high frequencies is made. The total absorption cross section of the black hole is obtained as a function of the energy. It presents behavior characteristic of a diffraction pattern. The constant geometric-optics limit [$\left(\frac{27}{4}\right)\pi r_s^{}{}_{}{}^2$] is approached in an oscillatory fashion. The physical interpretation of these results is given and a simple model which describes qualitatively the absorption of waves by the black hole is presented. From these absorption parameters, the Hawking emission rates are calculated and their properties discussed.