Related papers: Two-dimensional approach to relativistic positioni…
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…
In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space-time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are…
The relative geodesic motion on $(1+3)$-dimensional anti-de Sitter spacetimes is studied in terms of conserved quantities by adapting the Nachtmann boosting method created initially for the de Sitter spacetimes. In this approach the…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
After having shown that the corresponding components of a four vector transform via the same transformation factors as the space-time coordinates of the same event do, we design a relativistic diagram that displays in true values theirs…
The topic of this paper is to study the two way time-transfer problem between a ground based station and a low orbit Earth's satellite, in the aim of an application to the T2L2 experiment. The sudy is driven in a fully relativistic…
A relativistic self-gravitating equilibrium system with steady flow as well as spherical symmetry is discovered. The energy-momentum tensor contains the contribution of a current related to the flow and the metric tensor does an…
A simple method to generate a two-dimensional binary grid pattern, which allows for absolute and accurate self-location in a finite planar region, is proposed. The pattern encodes position information in a local way so that reading a small…
We introduce a relativistic splitting structure as a means to map fields and equations of electromagnetism from curved four-dimensional space-time to three-dimensional observer's space. We focus on a minimal set of mathematical structures…
If a clock, mathematically modeled by a parametrized timelike curve in a general-relativistic spacetime, is given, the radar method assigns a time and a distance to every event which is sufficiently close to the clock. Several geometric…
This talk discusses various aspects of the structure of space-time presenting mechanisms leading to the explanation of the "rigidity" of the manifold and to the emergence of time, i.e. of the Lorentzian signature. The proposed ingredient is…
This is the second paper on a new formalism for relativistic quantum measurements. Here, we construct a fully relativistic model for detectors that takes into account the detector's state of motion, intrinsics dynamics, initial states and…
This paper studies 3-D distributed network localization using mixed types of local relative measurements. Each node holds a local coordinate frame without a common orientation and can only measure one type of information (relative position,…
In the context of relativistic positioning, the coordinates of a given user may be calculated by using suitable information broadcast by a 4-tuple of satellites. Our 4-tuples belong to the Galileo constellation. Recently, we estimated the…
Analytical treatment of time transfer problem for Earth-Satellite system is presented. The development was made in a complete relativistic framework. In accordance with modern clock precision and for low altitude orbits, we neglect the…
The Earth's geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to…
A new approach to special relativity is presented which introduces coordinate systems with imaginary time axes, observation systems, and coordinate bases.
The harmonic oscillator plays a central role in physics describing the dynamics of a wide range of systems close to stable equilibrium points. The nonrelativistic one-dimensional spring-mass system is considered a prototype representative…
We develop a systematic procedure of finding integrable ''relativistic'' (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First,…
The project SYPOR wishes to use the global navigation satellite system GALILEO as an autonomous relativistic positioning system for the Earth. Motivations and a sketch of the basic concepts underlying the project are presented. For non…