# Black Holes: Scatterers, Absorbers and Emitters of Particles

## Abstract

Accurate and powerful computational methods developped by the author, based on the analytic resolution of the wave equation in the black hole background, 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) for a wide range of energy and angular momentum, the angular distribution of absorbed and scattered waves, and the Hawking emission rates. The total absorption spectrum of waves by the Black Hole is known exactly. It presents as a function of frequency a remarkable **oscillatory** behaviour characteristic of a diffraction pattern. It oscillates around its optical geometric limit \(
\left( {\tfrac{{27}}
{4}\pi r_s ^2 } \right)
\) 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: interference takes place between the absorbed rays arriving at the origin by different optical paths.

These fundamental features of the Black Hole Absorption 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 devoted to compute 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.

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