Scattering of massless fermions by Schwarzschild and Reissner-Nordström black holes

Abstract

In this paper we are studying the scattering of massless Dirac fermions by Schwarzschild and Reissner-Nordström black holes. This is done by applying the partial wave analysis to the scattering modes obtained after solving the massless Dirac equation in the asymptotic regions of the two black hole geometries. We succeed to obtain analytic phase shifts with the help of which the scattering cross section is computed. The glory and spiral scattering phenomena are showed to be present like in the case of massive fermion scattering by black holes.

Scattering of Dirac fermions by spherical massive bodies

“…We use an analytical method based on the asymptotic approximation of the radial functions that allows us to derive for the first time closed formulas of the phase shifts and scattering amplitudes in the case of the total reflection on a massive body. Thus we complete our analytical study devoted to the fermion scattering from black holes [11][12][13] obtaining new formulas which are in accordance with our previous results.…”

“…For starting our study we consider the asymptotic forms of our solutions (12) and (13) in which the integration constants play the role of free parameters. It is convenient to separate the general normalization constant N κ in Eqs.…”

“…Substituting this approximation of the Whittaker functions in Eqs. (12) and (13) and neglecting the terms of the order O( 1 x 2 ) we obtain the asymptotic solutions used herê…”

Scattering of spin half quantum fields by a Kiselev black hole

“…Furthermore, a neutral massless Dirac field on Reissner-Nordström also dose not have eQ/r terms and using the same mapping of the metric the case of a neutral Dirac field on Reissner-Nordström is obtained. This scenario was studied in our previous paper [55].…”

Solutions of the Dirac Equation in a Bardeen Black Hole Geometry

“…However, we will use here another gauge first defined in [30] and later developed in [26,32,33] that proved to be very useful in studying the Dirac equation in curved backgrounds [7,26,31,32,33,34,35,36,37]. This gauge, called the Cartesian gauge, is defined in spherical coordinates by the following tetrad fields: In this gauge the Dirac eq.…”