Fermions scattering in a three dimensional extreme black hole background

TL;DR

This paper calculates the fermion scattering cross section in an extreme BTZ black hole background, confirming it vanishes like scalar particles, and discusses the implications for black hole entropy and scattering space.

Contribution

It demonstrates that fermion scattering cross section vanishes for extreme BTZ black holes and introduces reciprocal space as the scattering domain in AdS spacetime.

Findings

Fermion absorption cross section is zero for extreme BTZ black holes.

The flux near the horizon is zero, consistent with vanishing entropy.

Reciprocal space provides a consistent framework for scattering analysis.

Abstract

The absorption cross section for scattering of fermions off an extreme BTZ black hole is calculated. It is shown that, as in the case of scalar particles, an extreme BTZ black hole exhibits a vanishing absorption cross section, which is consistent with the vanishing entropy of such object. Additionally, we give a general argument to prove that the particle flux near the horizon is zero. Finally we show that the {\it reciprocal space} introduced previously in \cite{gm} gives rise to the same result and, therefore, it could be considered as the space where the scattering process takes place in an AdS spacetime.