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

Abstract

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