Mapping Cartesian Coordinates into Emission Coordinates: some Toy Models

Abstract

After briefly reviewing the relativistic approach to positioning systems based on the introduction of the emission coordinates, we show how explicit maps can be obtained between the Cartesian coordinates and the emission coordinates, for suitably chosen set of emitters, whose world-lines are supposed to be known by the users. We consider Minkowski space-time and the space-time where a small inhomogeineity is introduced (i.e. a small "gravitational" field), both in 1+1 and 1+3 dimensions.Comment: 13 pages, 7 figures, Accepted for publication in International Journal of Modern Physics