Related papers: Physical frames along circular orbits in stationar…
Some conceptual issues concerning $f(T)$ theories --a family of modified gravity theories based on absolute parallelism-- are analyzed. Due to the lack of local Lorentz invariance, the autoparallel frames satisfying the field equations are…
We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner-Nordstr\"om, Kerr, and Kerr-Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider…
Binary collisions in Fermi systems obey two fundamental symmetries corresponding to the space and time inversion and to the interchange of particles and holes. We show that beyond the local and instant approximation of scattering-in and…
In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and…
Well-known results demonstrate the uniqueness of extremal isolated horizons (equivalently near-horizon spacetimes) in (3+1)-dimensions. This paper briefly reviews some of these results and then explicitly constructs families of…
We present a method for constructing all bounded rational motions that frame a space curve $\mathbf{r}(t)$. This means that the motion guides an orthogonal frame along the curve such that one frame axis is in direction of the curve tangent.…
In the present article we find a new class of solutions of Einstein's field equations. It describes stationary, cylindrically symmetric spacetimes with closed timelike geodesics everywhere outside the symmetry axis. These spacetimes contain…
The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and…
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating between pairs of bodies located on the coordinate axes.…
The paper addresses kinematic and geometrical aspects of the Orthoglide, a three-DOF parallel mechanism. This machine consists of three fixed linear joints, which are mounted orthogonally, three identical legs and a mobile platform, which…
We present the proper co-frame and its corresponding (diagonal) co-frame/spin connection pair for spherically symmetric geometries which can be used as an initial ansatz in any theory of teleparallel gravity. The Lorentz transformation…
Matter collineations of locally rotationally symmetric spacetimes are considered. These are investigated when the energy-momentum tensor is degenerate. We know that the degenerate case provides infinite dimensional matter collineations in…
Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi…
A simple, though rarely considered, thought experiment on relativistic rotation is described in which internal inconsistencies in the theory of relativity seem to arise. These apparent inconsistencies are resolved by appropriate insight…
Non-time-orthogonal analysis of rotating frames is applied to objects in gravitational orbits and found to be internally consistent. The object's surface speed about its axis of rotation, but not its orbital speed, is shown to be readily…
We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial…
Conditions for the existence of a gyroscope in spaces with affine connections and metrics are found. They appear as special types of Fermi-Walker transports for vector fields, lying in a subspace, orthogonal to the velocity vector field of…
Recursive matrix relations for kinematics and dynamics of the Orthoglide parallel robot having three concurrent prismatic actuators are established in this paper. These are arranged according to the Cartesian coordinate system with fixed…
A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant…