Scattering of spinning test particles by plane gravitational and electromagnetic waves

Abstract

The Mathisson–Papapetrou–Dixon (MPD) equations for the motion of electrically neutral massive spinning particles are analysed, in the pole–dipole approximation, in an Einstein–Maxwell plane-wave background spacetime. By exploiting the high symmetry of such spacetimes these equations are reduced to a system of tractable ordinary differential equations. Classes of exact solutions are given, corresponding to particular initial conditions for the directions of the particle spin relative to the direction of the propagating background fields. For Einstein–Maxwell pulses a scattering cross-section is defined that reduces, in certain limits, to those associated with the scattering of scalar and Dirac particles based on classical and quantum field theoretic techniques. The relative simplicity of the MPD approach and its use of macroscopic spin distributions suggests that it may have advantages in those astrophysical situations that involve strong classical gravitational and electromagnetic environments.