Ultra-relativistic fermion scattering by slowly rotating gravitational sources

In this paper, we discuss the gravitational scattering of fermions in the gravitational field of a massive, slowly rotating source characterized by an arbitrary spin orientation. We derive the gravito-electromagnetic field of the source using the weak-field approximation of Einstein's equations, which holds true when dealing with sources having a weak gravitational field and non-relativistic rotation. In such a gravitational background, we obtain the linearized fermion interaction Lagrangian. We then evaluate at the tree level the transition amplitude and the cross-section of the fermion scattering process in the ultra-relativistic limit (m << E). We examine the dependence of the cross-section on the relative orientation between the source spin and the direction of the fermion flux and discuss the contributions deriving from the gravitoelectric and the gravitomagnetic parts of the background field of the source. Further insight into the underlying physics is gained by comparing the results with those obtained in the case of gravitational scattering of a massless scalar field. We also find evidence of non-null backscattering in the case of orthogonality between the direction of propagation of the fermion flux and the source spin. (paper)