Non-relativistic Geodesic Behaviors for a Massive Charged Particle   Falling in de Sitter Spacetime
  In this article, continuing the work done in the previous paper (M. Fathi 2012), we apply a Lagrangian formalism to demonstrate the shape of the geodesic motion for a massive charged particle which is falling freely in a de Sitter spacetime. We will show that a spiral shape of the trajectory is available, due to the logarithmic behavior of time, with respect to the proper time. 
Farrin Payandeh, Mohsen Fathi
physics.gen-ph