Related papers: G\"odel spacetime, planar geodesics and the M\"obi…
We investigate the geodesics' kinematics and dynamics in the Linet-Tian metric with Lambda<0 and compare with the results for the Levi-Civita metric, when Lambda=0. This is used to derive new stability results about the geodesics' dynamics…
Many data analysis problems can be cast as distance geometry problems in \emph{space forms} -- Euclidean, spherical, or hyperbolic spaces. Often, absolute distance measurements are often unreliable or simply unavailable and only proxies to…
We explore two properties of backward orbits under semigroups of holomorphic self-maps in the unit disk. First, we prove that regular backward orbits are quasi-geodesics for the hyperbolic distance of the unit disk. Then, we show that…
A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
In general relativity, the motion of an extended body moving in a given spacetime can be described by a particle on a (generally non-geodesic) worldline. In first approximation, this worldline is a geodesic of the underlying spacetime, and…
The relative geodesic motion in central charts (i.e. static and spherically symmetric) on the $(1+3)$-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the…
We consider geodesics motion in a particular Kundt type III spacetime in which Einstein-Yang-Mills equations admit solutions. On a particular surface as constraint we project the geodesics into the (x,y) plane and treat the problem as a…
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion.…
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…
A conformal structure on a manifold $M^n$ induces natural second order conformally invariant operators, called M\"obius and Laplace structures, acting on specific weight bundles of $M$, provided that $n\ge 3$. By extending the notions of…
We study the G\"odel universe through worldlines associated with motion at constant speed and constant acceleration orthogonal to the instantaneous velocity (WSAs). We show that these worldlines can be used to access every region -- both…
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,…
The geodesic orbit property is useful and interesting in Riemannian geometry. It implies homogeneity and has important classes of Riemannian manifolds as special cases. Those classes include weakly symmetric Riemannian manifolds and…
In this contribution, the motion of unitary mass test particles in a perturbed Kerr-like metric is studied using simulations in the configuration and phase space. Our metric represents the approximate exterior spacetime of a massive…
The geodesics in various spherical Rindler frames are investigated. A display of some kinematical quantities of the spacetime is given. The constant acceleration from the metric acts as the surface gravity of the horizon $r = 0$. The radial…
This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034, gr-qc/9603022, gr-qc/9609035, gr-qc/9609046]. The introduction of a prior, i.e., predynamical global geometry of spacetime manifold is substantiated, and the geometry…
Here we consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with $\Omega^{\hat{r}}$, $\Omega^{\hat{\varphi}}$, and $\Omega^{\hat{\omega}}$ in a particular region of parameter space…
We study the geodesic motion in a space-time describing a swirling universe. We show that the geodesic equations can be fully decoupled in the Hamilton-Jacobi formalism leading to an additional constant of motion. The analytical solutions…
Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the…