The motion of a relativistic charged particle in a homogenous electromagnetic field in De-Sitter space

Abstract

We discuss the geometric characterization of the trajectoryof a moving charged particle, for the case of a homogeneous electromagnetic eld, in De-Sitter space when the motion is governed by the Lorentz equa-tion. We employ totally relativistic approach during the discussion and itis based on a systematic use of the four-dimensional Frenet-Serret formulae,which is adapted to the De-Sitter space to determine the worldline geometryof the electromagnetic eld acting on the particle in De-Sitter space, and ofthe Faraday antisymmetric tensor properties.