Non-relativistic Geodesic Behaviors for a Massive Charged Particle Falling in de Sitter Spacetime

TL;DR

This paper uses a Lagrangian approach to analyze the geodesic motion of a massive charged particle falling in de Sitter spacetime, revealing a spiral trajectory due to logarithmic time behavior.

Contribution

It introduces a Lagrangian formalism to describe geodesic paths of charged particles in de Sitter space, highlighting a spiral motion pattern.

Findings

Spiral shape of particle trajectories in de Sitter spacetime.

Logarithmic relationship between proper time and coordinate time.

Extension of previous work on particle motion in curved spacetime.

Abstract

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.