Positioning systems in Minkowski spacetime: from emission to inertial coordinates

Bartolomé Coll (1) , Joan Josep Ferrando (1) , Juan Antonio (1) , Morales -Lladosa (1)

1 Departament d'Astronomia i Astrofsica, Universitat de València

The coordinate transformation between emission coordinates and inertial coordinates in Minkowski space-time is obtained for arbitrary configurations of the emitters. It appears that a positioning system always generates two different coordinate domains, namely, the front and the back emission coordinate domains. For both domains, the corresponding covariant expression of the transformation is explicitly given in terms of the emitter world-lines. This task requires the notion of orientation of a emitter configuration. The orientation is shown to be computable from the emission coordinates for the users of a 'central ' region of the front emission coordinate domain. Other space-time regions associated with the emission coordinates are also outlined.

Mots clés: 04.20.-q; 45.20.Dd; 04.20.Cv; 95.10.Jk

Bartolomé Coll, Joan Josep Ferrando, Juan Antonio, Morales -Lladosa. Positioning systems in Minkowski spacetime: from emission to inertial coordinates. Classical and Quantum Gravity, 2010, 27 (6), pp.65013. ⟨10.1088/0264-9381/27/6/065013⟩. ⟨hal-00578463⟩