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. 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, and 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.

We propose a new formula to explain circular velocity profiles of spiral galaxies obtained from the Starobinsky model in the Palatini formalism. It is based on the assumption that the gravity can be described by two conformally related metrics: one of them is responsible for the measurement of distances, while the other, the so-called dark metric, is responsible for a geodesic equation and therefore can be used for the description of the velocity profile. The formula is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey (THINGS).

The asymptotic form of Dirac spinors in the field of the Reissner-Nordström black hole is derived for the scattering states (with E > mc 2 ) obtaining the phase shifts of the partial wave analysis of Dirac fermions scattered from charged black holes. Elastic scattering and absorption are studied giving analytic formulas for the partial amplitudes and cross sections. A graphical study is performed for analyzing the differential cross section (forward/backward scattering) and the polarization degrees as functions of the scattering angle.

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.

A new simple expression for the circular velocity of spiral galaxies is proposed and tested against HI Nearby Galaxy Survey (THINGS) data set. Its accuracy is compared with the one coming from MOND.