Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

TL;DR

This paper investigates the existence of closed particle trajectories on null curves in anti-de Sitter 3-space, providing explicit formulas and proving infinitely many such closed trajectories exist.

Contribution

It introduces a new particle model based on null curves in anti-de Sitter space and demonstrates the existence of infinitely many closed trajectories with explicit solutions.

Findings

Explicit formulas for particle trajectories are derived.

Infinitely many closed trajectories are proven to exist.

The model advances understanding of null curve dynamics in anti-de Sitter space.

Abstract

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.