de Sitter geodesics

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-Lemaître-Robertson-Walker, de Sitter-Painlevé 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.

18 pages, 6 figures

References in corpus (9)

• de Sitter special relativity
• Polarized Dirac fermions in de Sitter spacetime
• Special Relativity in the 21${}^{\mathrm{st}}$ century
• External symmetry in general relativity
• The physical meaning of the de Sitter invariants
• Conservation laws and scattering for de Sitter classical particles
• Rest frames and relativistic effects on de Sitter spacetimes
• Anti-de Sitter relativity
• Physical meaning of the conserved quantities on anti-de Sitter geodesics

Cited by in corpus (7)

• Light from Schwarzschild Black Holes in de Sitter expanding universe
• Kinematics in spatially flat FLRW space-time
• Longitudinal Doppler effect in de Sitter expanding universe
• Quantum theory of redshift in de Sitter expanding universe
• de Sitter geodesics in stereographic charts
• Solvable two-particle systems with time-asymmetric interactions in de Sitter space
• Collective classical motion on hyperbolic spacetimes of any dimensions