de Sitter relativity in central charts

TL;DR

This paper investigates the motion of particles in de Sitter spacetime using central charts, deriving conserved quantities and isometries, and analyzing relativistic effects like time dilation and Lorentz contraction.

Contribution

It introduces a detailed analysis of geodesic motion and Lorentz transformations in de Sitter spacetime within central charts, highlighting unique relativistic features.

Findings

Derived Lorentzian isometries relating different coordinate charts.

Analyzed time dilation and Lorentz contraction in de Sitter relativity.

Identified notable features of relativistic effects in curved spacetime.

Abstract

The relative geodesic motion in central charts (i.e. static and spherically symmetric) on the $(1+3)$-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart considered as the rest frame of a massive paticle freely moving on a timelike geodesic. The time dilation and Lorentz contraction are discussed pointing out some notable features of the de Sitter relativity in central charts.