Anti-de Sitter relativity

Abstract

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 the de Sitter spacetimes. In this approach the Lorentzian isometriy 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 them the problems of twin paradox and Lorentz contraction are solved.

12 pages, 4 figures, accepted for publication in PRD

References in corpus (8)

• External symmetry in general relativity
• The physical meaning of the de Sitter invariants
• The normalized energy eigenspinors of the Dirac field on anti-de Sitter spacetime
• The bizarre anti-de Sitter spacetime
• Rest frames and relativistic effects on de Sitter spacetimes
• Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius
• Physical meaning of the conserved quantities on anti-de Sitter geodesics
• Classical Oscilators in General Relativity

Cited by in corpus (6)

• Analysis of scalar and fermion quantum field theory on anti-de Sitter space-time
• de Sitter geodesics
• de Sitter relativity in central charts
• Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Liénard-Wiechert fields
• de Sitter geodesics in stereographic charts
• Collective classical motion on hyperbolic spacetimes of any dimensions