Fermion scattering by a Schwarzschild black hole

TL;DR

This paper investigates how massive spin-half particles scatter off a Schwarzschild black hole, combining analytical perturbation theory, classical geodesic approximations, and numerical methods to compute cross sections and polarization effects.

Contribution

It extends perturbation theory to higher order, derives glory scattering approximations, and develops a numerical approach for solving the Dirac equation in black hole backgrounds.

Findings

Calculated absorption and scattering cross sections.

Analyzed polarization effects during scattering.

Validated numerical results against theoretical models.

Abstract

We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. We begin by extending a recent perturbation theory calculation to next order to obtain Born series for the differential cross section and Mott polarization, valid at small couplings. We continue by deriving an approximation for glory scattering of massive spinor particles by considering classical timelike geodesics and spin precession. Next, we formulate the Dirac equation on a black hole background, and outline a simple numerical method for finding partial wave series solutions. Finally, we present our numerical calculations of absorption and scattering cross sections and polarization, and compare with theoretical expectations.