Discrete relativistic positioning systems

We discuss the design for a discrete, immediate, simple relativistic positioning system (rPS) which is potentially able of self-positioning (up to isometries) and operating without calibration or ground control assistance. The design is discussed in 1 + 1 spacetimes, in Minkowski and Schwarzschild solutions, as well as in 2 + 1 spacetimes in Minkowski. The system works without calibration, i.e. clock synchronizations, or prior knowledge about the motion of clocks, it is robust, i.e. it is able to test hypotheses break down (for example, if one or more clocks temporarily become not-freely falling, or the gravitational field changes), and then it is automatically back and operational when the assumed conditions are restored. In the Schwarzschild case, we also check that the system can best fit the gravitational mass of the source of the gravitational field. We stress that no weak field assumptions are made anywhere. In particular, the rPS we propose can work in a region close to the horizon since it does not use approximations or PPN expansions. More generally, the rPS can be adapted as detectors for the gravitational field and we shall briefly discuss their role in testing different theoretical settings for gravity. In fact, rPS is a natural candidate for a canonical method to extract observables out of a gravitational theory, an activity also known as designing experiments to test gravity