Related papers: Geometry of an accelerated rotating disk
We show that any second order dynamic equation on a configuration space $X\to R$ of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle $TX\to X$ of relativistic…
The force of adhesion of a rotationally symmetric indenter and an elastic half-space is analyzed analytically and numerically using an extension of the method of dimensionality reduction (MDR) for superimposed normal/tangential adhesive…
First-order Fermi acceleration process at a relativistic shock wave is investigated by means of Monte Carlo simulations involving numerical integration of particle equations of motion in a turbulent magnetic field near the shock. In…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\to X$ of…
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
A gravitational theory with derivative matter coupling is proposed which adopt de Sitter expansion at late times with ordinary baryonic matter. Matter components are conserved separately in the cosmological background and the Newtonian…
Two families of models of rotating relativistic disks based on Taub-NUT and Kerr metrics are constructed using the well-known "displace, cut and reflect" method. We find that for disks built from a generic stationary axially symmetric…
While a growing body of research indicates that relativistic magnetic reconnection is a prodigious source of particle acceleration in high-energy astrophysical systems, the dominant acceleration mechanism remains controversial. Using a…
The existence of "dark matter", inferred from the observed rotation curves of galaxies, is a hypothesis which is widely regarded as problematic. This paper proposes an alternative hypothesis based on the space-time geometry near a rotating…
In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial…
In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…
We investigate torsion and noninertial effects on a spin-$1/2$ quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference…
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative…
General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…
The Lorentzian spacetime metric is replaced by an area metric which naturally emerges as a generalized geometry in quantum string and gauge theory. Employing the area metric curvature scalar, the gravitational Einstein-Hilbert action is…
The aim of the article is to find a transformation that links the local affine velocity of a non-rigid body in the laboratory inertial reference frame $ S $ with the centro-affine velocity of motion of this body in the accompanying…
We introduce a characterization of disclination lines in three dimensional nematic liquid crystals as a tensor quantity related to the so called rotation vector around the line. This quantity is expressed in terms of the nematic tensor…
Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…