de Sitter relativity in central charts

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.

20 pages, 2 figure. to be published in EPJC. arXiv admin note: text overlap with arXiv:1706.01785

References in corpus (4)

• Special Relativity in the 21${}^{\mathrm{st}}$ century
• The physical meaning of the de Sitter invariants
• Conservation laws and scattering for de Sitter classical particles
• Anti-de Sitter relativity