Scattering in three-dimensional extremal black holes

An approach to scattering theory in three-dimensional AdS spaces is propose d. Firstly, we consider the scattering of spinless relativistic particles b y a three-dimensional extremal black hole and compute the absorption cross section sigma (abs) = J(abs)/J(infinity) without using in and out states. S econdly, we posit a reciprocal space H where in and out states and the scat tering amplitude are defined as in usual scattering theory. We show that bo th descriptions are equivalent and H could be considered as the space where the scattering processes in AdS should be defined.