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I review, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie…
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a…
A theoretical framework for emission originating from rapidly rotating oblate compact objects is described in detail. By using a Hamilton-Jacobi formalism, we show how the special relativistic rotational effects such as aberration of…
We present a new simple relativistic model for planetary motion describing accurately the anomalous precession of the perihelion of Mercury and its origin. The model is based on transforming Newton's classical equation for planetary motion…
We give an elementary proof of a formula expressing the rotation number of a cyclic unimodular sequence of lattice vectors in terms of arithmetically defined local quantities. The formula has been originally derived by A. Higashitani and M.…
The motion of a magnetic spin particle in electromagnetic fields is considered on the basis of general principles of the classical relativistic theory. Alternative approaches in derivation of the equations of charge motion and spin…
We extend a recent approach to Deformed Special Relativity based on deformed dispersion laws, entailing modified Lorentz transformations and, at the same time, noncommutative geometry and intrinsically discrete spacetime. In so doing we…
Besides the defining space-time symmetries (homogeneity and isotropy) of inertial frames, the derivation of Lorentz transformation requires postulating the principle of relativity and the existence of a finite speed limit. In this article,…
An elementary pedagogical derivation of the Lense-Thirring precession is given based on the use of Hamilton vector. The Hamilton vector is an extra constant of motion of the Kepler/Coulomb problem related simply to the more popular…
We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations.…
One of the many surprising results found in the mechanics of rotating systems is the stabilization of a particle in a rapidly rotating planar saddle potential. Besides the counterintuitive stabilization, an unexpected precessional motion is…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
The relativistic precession can be quickly inferred from the nonlinear polar orbit equation without actually solving it.
The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising…
Context. High accuracy astrometric instruments like Gaia aiming at an accuracy of 1 microarcsecond cannot be considered as point-like observers in the framework of relativistic modelling of observable quantities. Aims. Special-relativistic…
Doubly Special Relativity is usually formulated in momentum space, providing the explicit nonlinear action of the Lorentz transformations that incorporates the deformation of boosts. Various proposals have appeared in the literature for the…
In this paper I argue for a reassessment of special relativity. The fundamental theory of relativity applicable in this Universe has to be consistent with the existence of the massive Universe, and with the effects of its gravitational…
We derive the perihelion precession of planetary orbits using quantum field theory extending the Standard Model to include gravity. Modeling the gravitational bound state of an electron via the Dirac equation of unified gravity [Rep. Prog.…