Partial wave analysis of the Dirac fermions scattered from Schwarzschild black holes

Abstract

Asymptotic analytic solutions of the Dirac equation, giving the scattering modes (of the continuous energy spectrum, $E>mc^2$) in Schwarzschild's chart and Cartesian gauge, are used for building the partial wave analysis of Dirac fermions scattered by black holes. The contribution of the bound states to absorption and possible resonant scattering is neglected because of some technical difficulties related to the discrete spectrum that is less studied so far. In this framework, the analytic expressions of the differential cross section and induced polarization degree are derived in terms of scattering angle, mass of the black hole, energy and mass of the fermion. Moreover, the closed form of the absorption cross section due to the scattering modes is derived showing that in the high-energy limit this tends to the event horizon area regardless of the fermion mass (including zero). A graphical study presents the differential cross section analyzing the forward/backward scattering (known also as glory scattering) and the polarization degree as functions of scattering angle. The graphical analysis shows the presence of oscillations in scattering intensity around forward/backward directions, phenomena known as spiral scattering. The energy dependence of the differential cross section is also established by using analytical and graphical methods.