Related papers: Positioning systems in Minkowski space-time: Bifur…
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…
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…
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating…
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…
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…
A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed repetition period in its rest frame.) The positioning system uses the fact that an…
We give a closed expression for the Minkowski (1+1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform…
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…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz…
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…
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…
The worldline of a uniformly accelerated localized observer in Minkowski space is restricted in the Rindler wedge, where the observer can in principle arrange experiments repeatedly, and the Cauchy problem for quantum fields in that Rindler…
We consider the $\varrho$-Minkowski spacetime, a model with linear noncommutativity involving the time and the azimuthal angle. We study its quantum symmetries, the $\varrho$-Poincar\'e quantum group, and analyse the concepts of…
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…
Orientability is an important topological property of spacetime manifolds. It is generally assumed that a test for spatial orientability requires a journey across the whole 3-space to check for orientation-reversing paths. Since such a…
Physicists have been interested in accelerated observers for quite some time. Since the advent of special relativity, many authors have tried to understand these observers in the framework of Minkowski spacetime. One of the most important…
Position determination of photon emitters and associated strong field parallax effects are investigated using relativistic optics when the photon orbits are confined to the equatorial plane of the Schwarzschild spacetime. We assume 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…
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true…
A general approach to the problem of positioning by means of pulsars or other pulsating sources located at infinity is described. The counting of the pulses for a set of different sources whose positions in the sky and periods are assumed…