# Anti-de Sitter relativity

## TL;DR

This paper develops a comprehensive framework for understanding relative geodesic motion in anti-de Sitter spacetimes using conserved quantities and adapted boosting methods, addressing classical relativity problems.

## Contribution

It introduces a novel approach to analyze geodesic motion in anti-de Sitter space, including derivation of Lorentzian isometries and transformation of conserved quantities.

## Key findings

- Derived Lorentzian isometry for anti-de Sitter spacetime.
- Solved twin paradox and Lorentz contraction in this context.
- Established a complete theory of relative geodesic motion.

## 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.