de Sitter geodesics

TL;DR

This paper analyzes geodesics in 4D de Sitter spacetime across various coordinate charts, revealing how conserved quantities determine their parameters and identifying a special static chart where geodesics form hyperbolas with asymptotes linked to conserved momenta.

Contribution

It provides a detailed study of geodesic parameters in different de Sitter charts and introduces a unique static chart where geodesics are hyperbolas with specific asymptotic properties.

Findings

Geodesic parameters are determined by conserved quantities in various charts.

Existence of a special static chart with hyperbolic geodesics.

Geodesics asymptote to lines defined by conserved momentum.

Abstract

The geodesics on the $(1+3)$-dimensional de Sitter spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lema\^itre-Robertson-Walker, de Sitter-Painlev\'e and static local charts with Cartesian space coordinates. Moreover, it is shown that there exist a special static chart in which the geodesics are genuine hyperbolas whose asymptotes are given by the conserved momentum and the associated dual momentum.