Scattering in Three Dimensional Extremal Black Holes

TL;DR

This paper develops a scattering theory framework for particles interacting with three-dimensional extremal black holes in AdS space, introducing a reciprocal space approach that aligns with traditional scattering concepts.

Contribution

It introduces a reciprocal space formalism for scattering in 3D extremal black holes, establishing equivalence with conventional descriptions without relying on in/out states.

Findings

Derived the absorption cross section without in/out states

Proposed a reciprocal space for scattering processes in AdS

Established the equivalence of two scattering descriptions

Abstract

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 $\sigma_{abs} =J_{abs}/J_{\infty}$ without using {\it in} and {\it out} states. Secondly, we posit a reciprocal space ${\cal H}$ 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 ${\cal H}$ could be considered as the space where the scattering processes in AdS should be defined.