Scattering in Three Dimensional Extremal Black Holes

An approach to scattering theory in three dimensional AdS spaces is proposed. Firstly we consider the scattering of spinless relativistic particles by a three dimensional extremal black hole and compute the absorption cross section ${\sigma }_{abs}=J_{abs}\mathrm{/}{J}_{\mathrm{\infty }}$ without using {\it in} and {\it out} states. Secondly, we posit a reciprocal space $\mathcal{H}$ where {\it in} and {\it out} states and the scattering amplitude is defined as in usual scattering theory. We show that both descriptions are equivalent and $\mathcal{H}$ could be considered as the space where the scattering processes in AdS should be defined.