Related papers: Geometry of an accelerated rotating disk
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
This article provides a self-contained pedagogical introduction to the relativistic kinetic theory of a dilute gas propagating on a curved spacetime manifold (M,g) of arbitrary dimension. Special emphasis is made on geometric aspects of the…
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal…
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…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
We study the space geometry of a rotating disk both from a theoretical and operational approach, in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an…
The relativistic acceleration of an electron in a uniform gravitational field is calculated numerically using the generalization of the Dirac equation to curved spacetime. Equivalent results are also obtained analytically using an iterative…
The geometry of the rotating disk is revisited and the quantum consequences are discussed. A suggestion to detect the presence of the Gaussian curvature on the rotating disk only measuring transition frequencies is made. A quantum…
We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities…
Differential geometry may be generalized to allow infinitesimals to any order. The purpose of the present contribution is to show that the theory so developed expands received geometrical ideas in an interesting way, rich in potential for…
We provide a method to compute the dimension of the tangent space to the global infinitesimal deformation functor of a curve together with a subgroup of the group of automorphisms. The computational techniques we developed are applied to…
We present a numerical method for computing the \textit{Fermi} and \textit{observational coordinates} of a distant test particle with respect to an observer. We apply this method for computing some previously introduced concepts of relative…
We find equations of particle motion from the point of view of observer on a rotating disk, and demonstrate that a particle moving along a rotating disk is influenced by forces arising from geometry. They can be considered as analogs of the…
In an arbitrary axisymmetric stationary spacetime, we determine the expression for the tangential velocity of test objects following a circular stable geodesic motion in the equatorial plane, as function of the metric coefficients. Next, we…
The classifying space of inertial reference frames in special relativity is naturally hyperbolic. There is a remarkable interplay between central elements of hyperbolic geometry and those of special relativity -- which, to a certain extent,…
This proceedings paper reports on the theoretical modelling of particle acceleration in magnetised turbulent plasmas. It briefly reviews some recent findings obtained from fully kinetic numerical simulations of large-amplitude, semi to…
We study the motion of charge carriers in curved Dirac materials, in the presence of a local Fermi velocity. An explicit parameterization of the latter emerging quantity for a nanoscroll cylindrical geometry is also provided, together with…
We explore thick accretion disks around rotating attractors. We detail the configurations analysing the fluid angular momentum and finally providing a characterization of the disk morphology and different possible topologies. Investigating…
The expansion of space, and other geometric properties of cosmological models, can be studied using geometrically defined notions of relative velocity. In this paper, we consider test particles undergoing radial motion relative to comoving…