Emission vs Fermi coordinates: applications to relativistic positioning systems

Abstract

A 4-dimensional relativistic positioning system for a general spacetime is constructed by using the so called "emission coordinates". The results apply in a small region around the world line of an accelerated observer carrying a Fermi triad, as described by the Fermi metric. In the case of a Schwarzschild spacetime modeling the gravitational field around the Earth and an observer at rest at a fixed spacetime point, these coordinates realize a relativistic positioning system alternative to the current GPS system. The latter is indeed essentially conceived as Newtonian, so that it necessarily needs taking into account at least the most important relativistic effects through Post-Newtonian corrections to work properly. Previous results concerning emission coordinates in flat spacetime are thus extended to this more general situation. Furthermore, the mapping between spacetime coordinates and emission coordinates is completely determined by means of the world function, which in the case of a Fermi metric can be explicitly obtained.

12 pages iop style, 2 eps figures, to appear on Classical and Quantum Gravity, 2008

References in corpus (5)

• GPS observables in general relativity
• Real null coframes in general relativity and GPS type coordinates
• Relativity of GPS Measurement
• Two-dimensional approach to relativistic positioning systems
• Positioning with stationary emitters in a two-dimensional space-time

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• Relativistic positioning: errors due to uncertainties in the satellite world lines
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• Static Observers in Curved Spaces and Non-inertial Frames in Minkowski Spacetime
• Mapping the spacetime metric with GNSS: a preliminary study
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