Gravitational scattering of massive particles on a background with axial symmetry

Abstract

Using the S-matrix formalism and the Feynman diagram technique, the gravitational scattering of the minimally and non-minimally coupled scalar, spinor, vector, spin-vector, and spin-2 massive particles, in a background described by Kerr–Newman geometry is studied for any value of the scattering angle. We find that the differential cross sections of the scalar, spinor, and vector particles in the backward direction and ultrarelativistic case are finite and consequently the backscattered particles must have the opposite helicity, whereas for the spin-vector and spin-2 particles in the same case, the differential cross sections are clearly infinite. It has been shown, for the particular case when the angular momentum of the scatterer vanishes (i.e., for the Schwarzschild geometry) and in the small-angle approximation and ultrarelativistic limit as well, the differential cross sections are all of the same type, i.e., in this special limit case the gravitational particle scattering is spin independent. PACS Nos. 03.80+r, 11.80-m, 03.70+k