Related papers: Studying null and time-like geodesics in the class…
This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder like deformation in the background of the Kepler problem. In order to accomplish that task, a newtonian spacetime is…
We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test…
The teaching of general relativity at the secondary school and lower undergraduate university levels is necessarily based on approaches with a restricted use of mathematics. An important aspect of teaching general relativity at this level…
A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling…
We take a three dimensional Euclidian metric in toroidal coordinates and consider the corresponding Laplace equation. The simplest solution of this equation is taken. Based on this we build a Weyl space-time. This space-time is transformed…
Despite being a major component in the teaching of special relativity, the twin `paradox' is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often…
Semi-supervised 3D object detection, aiming to explore unlabeled data for boosting 3D object detectors, has emerged as an active research area in recent years. Some previous methods have shown substantial improvements by either employing…
It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
In the homogeneous metric of Som-Raychaudhuri, in general relativity, we study the three types of geodesics: timelike, null, and spacelike; in particular, the little known geodesics of simultaneities. We also study the non-geodetic circular…
While Newtonian gravity is an adequate model for current geophysical exploration, Einsteinian gravity, based on the connection between free fall and warped time, has superseded Newtonian gravity as our best understanding of the universe.…
Focus of this study is to explore some aspects of mathematical foundations for using complex manifolds as a model for space-time. More specifically, certain equations of motions have been derived as a Projective geodesic on a real manifold…
This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…
Visualizations that adopt a first-person point of view allow observation and, in the case of interactive simulations, experimentation with relativistic scenes. This paper gives examples of three types of first-person visualizations:…
The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined…
We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and…
Learning is a fundamental characteristic of living systems, enabling them to comprehend their environments and make informed decisions. These decision-making processes are inherently influenced by available information about their…
The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force…
Non-isotropic geometries are of interest to low-dimensional topologists, physicists and cosmologists. However, they are challenging to comprehend and visualize. We present novel methods of computing real-time native geodesic rendering of…
Mass redistribution on Earth due to dynamic processes such as ice melting and sea level rise leads to a changing gravitational field, observable by geodetic techniques. Monitoring this change over time allows us to learn more about our…