Related papers: Two-dimensional approach to relativistic positioni…
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic…
The theory of relativistic {\em location systems} is sketched. An interesting class of these systems is that of relativistic {\em positioning systems,} which consists in sets of four clocks broadcasting their proper time. Among them, the…
A {\em relativistic positioning system} consists in a set of four clocks broadcasting their respective proper time by means of light signals. Among them, the more important ones are the {\em auto-located positioning systems,} in which every…
The basic elements of Coll positioning systems (n clocks broadcasting electromagnetic signals in a n-dimensional space-time) are presented in the two-dimensional case. This simplified approach allows us to explain and to analyze the…
Emission relativistic coordinates are a class of spacetime coordinates defined and generated by four emitters (satellites, pulsars) broadcasting their proper time by radio signals. They are the main ingredient of the simplest conceivable…
We investigate a relativistic positioning system where the coordinates of the users are determined by the proper times broadcasted by clocks in motion in spacetime: these are the so-called emission coordinates. In particular, we focus on…
Relativistic positioning systems are interesting {\em technical objects} for applications around the Earth and in the Solar system. But above all else, they are basic {\em scientific objects} allowing developing relativity from its own…
Starting from the description of space-time as a curved four-dimensional manifold, null Gaussian coordinates systems as appropriate for relativistic positioning will be discussed. Different approaches and strategies will be reviewed,…
Fully relativistic coordinates have been proposed for (relativistically) running a "GPS" system. These coordinates are the arrival times of the light signals emitted by four "satellites" (clocks). Replacing the signals emitted by four…
Relativistic stereometric coordinates supplied by relativistic auto-locating positioning systems made up of four satellites supplemented by a fifth one are defined in addition to the well-known emission and reception coordinates. Such a…
This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated…
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\bf 73}, 084017 (2006); {\bf 74}, 104003 (2006)], where the possibility of making relativistic…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…
We present here a method for the relativistic positioning in spacetime based on the reception of pulses from sources of electromagnetic signals whose worldline is known. The method is based on the use of a four-dimensional grid covering the…
4 emitters broadcasting an increasing electromagnetic signal generate a system of relativistic coordinates for the space-time, called emission coordinates. Their physical realization requires an apparatus similar to the one of the Global…
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…
A natural two-metric formalism, generated by the world function of the space-time, is used. This circumstance admits one to localize the relative gravitational field, which is described by a tensor.
We extend to three dimensions the proposal of a completely relativistic positioning system (rPS). The system does not rely on approximations, in fact, it works at a few Schwarzschild radii from a black hole, and it does not rely on…
Flatness of discrete-time systems can be characterized by two simple properties. There exists a map, a submersion, from the flat coordinates and their forward shifts to the state and the input of the discrete-time system, such that the…