Anti-de Sitter relativity

摘要

The relative geodesic motion on (1 + 3)-dimensional anti-de Sitter spacetimes is studied in terms of conserved quantities by adapting the Nachtmann boosting method created initially for de Sitter spacetimes. In this approach the Lorentzian isometry is 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 mobile object moving on a timelike anti-de Sitter geodesic. The transformation of the conserved quantities is also investigated, constructing thus a complete theory of the relative geodesic motion on anti-de Sitter spacetimes. Some applications are discussed, among which the problems of twin paradox and Lorentz contraction are solved.