6533b7dcfe1ef96bd127293f

RESEARCH PRODUCT

Positioning systems in Minkowski space-time: from emission to inertial coordinates

Bartolomé CollJoan Josep FerrandoJuan AntonioMorales -Lladosa

subject

Physics04.20.Cv95.10.JkInertial frame of reference45.20.DdPhysics and Astronomy (miscellaneous)Positioning systemAstrophysics::High Energy Astrophysical PhenomenaCoordinate systemMathematical analysisFOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)Domain (mathematical analysis)General Relativity and Quantum Cosmology04.20.-qTransformation (function)Orientation (geometry)Minkowski spaceCovariant transformation

description

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 an 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.

yearjournalcountryeditionlanguage
2009-10-14
10.1088/0264-9381/27/6/065013http://arxiv.org/abs/0910.2568