Related papers: Geometry of an accelerated rotating disk
We develop a new method to determine the acceleration of a block sliding down along the face of a moving wedge. We have been able to link the solution of this problem to that of the inclined plane problem of elementary physics, thus…
In the last few decades, basic ideas of topology have completely transformed the prediction of quantum transport phenomena. Following this trend, we go deeper into the incorporation of modern mathematics into quantum material science…
Following Toomre & Kalnajs (1991), local models of slightly dissipative self-gravitating disks show how inhomogeneous structures can be maintained over several galaxy rotations. Their basic physical ingredients are self-gravity, dissipation…
We construct models for first- and second-order Fermi acceleration of particles, incorporating generic frame transformations, dispersion relations, and conservation laws. Within this framework, we study deformations of Lorentz symmetry via…
We propose a new approach to the study of rotational surfaces in Lorentz-Minkowski space based on the notion of the geometric linear momentum of the generatrix curves with respect to the axes of revolution. This technique allows us to…
Possible formulations of the problem of cosmic rays acceleration in the interstellar galactic medium are considered with the use of fractional differential equations. The applied technique has been physically justified. A Fermi result has…
The time dependent conformally-flat spherical Rindler spacetime is investigated. The geometry has an apparent horizon that coincides with the causal horizon. The scalar acceleration of a static observer is constant and equals to the…
A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well…
There is a vast literature showing the connection between a deformed relativistic kinematics and a curved momentum space, and, in particular, how the former can be obtained from the geometrical properties of the latter. However, there is…
A model of relativistic extended particle is considered with the help of generalization of space-time inter-val. Ten additional dimensions are connected with six rotational and four deformational degrees of freedom. An obtained…
In this series of papers I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable manifold, and their dimension is one unit…
We investigate the velocity field derived from HI measurements of the irregular galaxy ESO 358-60 using the Velocity Ring Model (VRM) method. This technique, which assumes a coplanar disk, allows us to reconstruct coarse-grained maps of…
We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of…
This work explores modified inertia in the context of galactic dynamics by investigating the consequences of introducing quantum-motivated bounds on acceleration. Building on earlier ideas related to maximal acceleration and quantum speed…
These are introductory notes on the study of the Dirac equation in curved spacetime and its relation to hidden symmetries of the dynamics. We present general results on the relation between special spacetime tensors and hidden symmetries,…
We discuss some aspects of the differential geometry of curves in Minkowski space. We establish the Serret-Frenet equations in Minkowski space and use them to give a very simple proof of the fundamental theorem of curves in Minkowski space.…
The classical and continuum limit of a quantum gravitational setting could lead, at mesoscopic regimes, to a very different notion of geometry w.r.t. the pseudo-Riemannian one of special and general relativity. A possible way to…
We study Weitzenb\"ock's torsion and discuss its properties. Specifically, we calculate the measured components of Weitzenb\"ock's torsion tensor for a frame field adapted to static observers in a Fermi normal coordinate system that we…
This thesis introduces the notion of "relative gerbes" for smooth maps of manifolds, and discusses their differential geometry. The equivalence classes of relative gerbes are classified by the relative integral cohomology in degree three.…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…