Black Holes: Scatterers, Absorbers and Emitters of Particles

Accurate and powerful analytic and computational methods developped by the author allow to obtain the highly non trivial total absorption spectrum of the Black Hole, as well as phase shifts and cross sections (elastic and inelastic), the angular distribution of absorbed and scattered waves, and the Hawking emission rates. The exact total absorption spectrum of waves by the Black Hole presents as a function of frequency a remarkable oscillatory behaviour characteristic of a diffraction pattern. It oscillates around its optical geometric limit (27/4) pi (r_s)^2 with decreasing amplitude and almost constant period. This is an unique distinctive feature of the black hole absorption, and due to its r=0 singularity. Ordinary absorptive bodies and optical models do not present these features. The Hamiltonian describing the wave-black hole interaction is non hermitian (despite being real) due to its singularity at the origin (r=0). The unitarity optical theorem of scattering theory is generalized to the black hole case explicitely showing that absorption takes place only at the origin (r = 0). All these results allow to understand and reproduce the Black Hole absorption spectrum in terms of Fresnel-Kirchoff diffraction theory. These fundamental features will be present for generic higher dimensional Black Hole backgrounds, and whatever the low energy effective theory they arise from. In recent and increasing litterature on absorption cross sections (`grey body factors') of black holes (whatever ordinary, stringy, D-braned), the fundamental remarkable features of the Black Hole Absorption spectrum are overlooked.Comment: LaTex, 19 pages, Lectures delivered at the Chalonge School, Nato ASI: Phase Transitions in the Early Universe: Theory and Observations. To appear in the Proceedings, Editors H. J. de Vega, I. Khalatnikov, N. Sanchez. (Kluwer Pub