Related papers: Emission vs Fermi coordinates: applications to rel…
Deviation equation: Second order differential equation for the 4-vector which measures the distance between reference points on neighboring world lines in spacetime manifolds. Relativistic geodesy: Science representing the Earth (or any…
Using the accepted methods to extract natural system behavior from the Einstein-Hilbert gravitational field tensor equation, a new coordinate transformation is analyzed. It is demonstrated that these extraction methods yield specific…
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…
It is shown that the Fermi-Walker gauge allows the general solution of determining the metric given the sources, in terms of simple quadratures. We treat the general stationary problem providing explicit solving formulas for the metric and…
A class of coordinate systems is found for Friedmann Cosmologies with local gravity such that it is possible to formulate quantum theory over astronomical and cosmological distances. When light from distance objects is treated as a quantum…
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…
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum…
Starting from the Einstein equations in Schwarzschild-de Sitter (SdS) spacetime and imposing Friedmann-Robertson-Walker coordinates at large distances, we find two coordinate systems with time-dependent metrics that are smooth across both…
Today, the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called "relativistic corrections", computed with the required precision using the Post-(Post-)Newtonian formalism. The current…
Gravity whose nature is fundamental to the understanding of solar system, galaxies and the structure and evolution of the Universe, is theorized by the assumption of curved spacetime, according to Einstein`s general theory of relativity…
The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for navigation is created by the discontinuities…
Fermi Normal Coordinates (FNC) are a useful frame for isolating the locally observable, physical effects of a long-wavelength spacetime perturbation. Their cosmological application, however, is hampered by the fact that they are only valid…
For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of…
The 3-space of a universe model is defined at a certain simultaneity. Hence space depends on which time is used. We find a general formula generating all known transformations to conformally flat spacetime coordinates, and work out the…
The Global Positioning System (GPS) provides an excellent educational example as to how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an…
Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation…
Recent modern space missions deliver invaluable information about origin of our universe, physical processes in the vicinity of black holes and other exotic astrophysical objects, stellar dynamics of our galaxy, etc. On the other hand,…
The formulation of General Relativity in which the 4-dimensional space-time is embedded in a flat host space of higher dimension is reconsidered. New classes of embeddings (modeled after Nash's classical free embeddings) are introduced.…
The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…
What does it mean to say that space expands? One approach to this question is the study of relative velocities. In this context, a non local test particle is "superluminal" if its relative velocity exceeds the local speed of light of the…