Related papers: Discrete Relativistic Positioning Systems
We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order…
We construct and parametrize solutions to the constraint equations of general relativity in a neighborhood of Minkowski spacetime with arbitrary prescribed decay properties at infinity. We thus provide a large class of initial data for the…
Higher-order theories of gravity have received much attention from several areas including quantum gravity, string theory and cosmology. This paper proposes a higher-order gravity whose action includes all curvature scalar terms up to the…
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…
Reconfigurable intelligent surfaces (RISs) are one of the most promising technological enablers of the next (6th) generation of wireless systems. In this paper, we introduce a novel use-case of the RIS technology in radio localization,…
We suggest a new relativity principle, which asserts the impossibility to distinguish the state of rest and the state of motion at the constant velocity of a system, if no work is done to the system in question during its motion. We suggest…
Pulsars are natural cosmic clocks. On long timescales they rival the precision of terrestrial atomic clocks. Using a technique called pulsar timing, the exact measurement of pulse arrival times allows a number of applications, ranging from…
The dissertation presents possibilities of applying noncommutative spacetimes description, particularly kappa-deformed Minkowski spacetime and Drinfeld's deformation theory, as a mathematical formalism for Doubly Special Relativity theories…
We present a new proof of linear stability of the Schwarzschild solution to gravitational perturbations. Our approach employs the system of linearised gravity in the new geometric gauge of \cite{benomio_kerr}, specialised to the $|a|=0$…
General Relativity (GR) is shown to be a complete theory with respect to the isochrony of the pendulum. This guarantees that time can be measured with a mechanical clock within the theory itself as a matter of principle. The proper and…
Nowadays, the Global Navigation Satellite Systems (GNSS), working like global positioning systems, are the GPS (NAVSTAR) and the GLONASS, which only are operative when several relativistic effects are corrected. In the next years the…
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…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
Humans can easily deduce the relative pose of a previously unseen object, without labeling or training, given only a single query-reference image pair. This is arguably achieved by incorporating i) 3D/2.5D shape perception from a single…
Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, special relativity uses the assumption about the Euclidean structures of gravity-free…
When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…
Consider a point set D with a measure function w : D -> R. Let A be the set of subsets of D induced by containment in a shape from some geometric family (e.g. axis-aligned rectangles, half planes, balls, k-oriented polygons). We say a range…
We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar, $R$, of arbitrary degree, $n$, in arbitrary dimension, $D$. The global properties of all such solutions are derived by…
We show that Doubly Special Relativity (DSR) can be viewed as a theory with energy-momentum space being the four dimensional de Sitter space. Different formulations (bases) of the DSR theory considered so far can be therefore understood as…
The concept of a physical space, which actualizes Euclidean geometry, is not confined to the statics of solids but extensible to the phenomena where Newtonian mechanics is valid, defining its concept of time. The laws of propagation of…