High‐Speed Scattering of Charged and Uncharged Particles in General Relativity

Abstract

After a brief consideration of the high‐speed scattering of two point charges we thoroughly discuss high‐speed scattering for a charged particle by a fixed mass and of two uncharged particles of comparable masses. We use perturbation technique over Minkowski spacetime in the de Donder gauge and solve the field equations and the resulting equations of motion (which take the reaction of the particles' quasistatic self‐field into account) by iteration. The obtained energy‐momentum conservation laws allow the computation of second‐order corrections for the scattering angle and the cross section. The asymptotic structure of the far‐field indicates synchrotron radiation (electromagnetic and gravitational, respectively) which causes an energy loss whose reaction on the motion is briefly considered in the low‐velocity limit including bound motion. (For neutral particles this is a third‐order effect). Copyright © 1985 WILEY‐VCH Verlag GmbH & Co. KGaA