Related papers: Superposition of Weyl solutions: circular orbits
The Poincare and Poincare-Weyl gauge theories of gravitation with Lagrangians quadratic on curvature and torsion in post-Riemannian spaces with the Dirac scalar field is discussed in a historical aspect. The various hypothesizes concerning…
In the standard Einstein's theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space-time. In this…
We study a simple analytic solution to Einstein's field equations describing a thin spherical shell consisting of collisionless particles in circular orbit. We then apply two independent criteria for the identification of circular orbits,…
We investigate static cylindrically symmetric vacuum solutions in Weyl coordinates in the framework of f(T) theories of gravity, where T is the torsion scalar. The set of modified Einstein equations is presented and the fourth coming…
We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type N vacuum solutions, which describe the radiation region of isolated gravitational systems with…
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…
On the basis of the Poincare-Weyl gauge theory of gravitation, a new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field representing the dark matter…
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the…
We consider a well-known static, axially symmetric, vacuum solution of Einstein equations belonging to Weyl's class and determine the fundamental frequencies of small harmonic oscillations of test particles around stable circular orbits in…
The role of a physical phase space structure in a classical and quantum dynamics of gauge theories is emphasized. In particular, the gauge orbit space of Yang-Mills theories on a cylindrical spacetime (space is compactified to a circle) is…
We propose to study the behavior of complicated numerical solutions to Einstein's equations for generic cosmologies by following the geodesic motion of a swarm of test particles. As an example, we consider a cylinder of test particles…
Using a recently developed generalized Weyl formalism, we construct an asymptotically flat, static vacuum Einstein solution that describes a superposition of multiple five-dimensional Schwarzschild black holes. The spacetime exhibits a…
Equatorial circular geodesic orbits of neutral test particles in the exterior spacetime of a charged rotating disc of dust are analyzed in dependence of its specific charge and a relativity parameter. The charged rotating disc of dust is an…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
We analyze the behaviour of geodesic motion of test particles in the spacetime of a specific class of axially symmetric static vacuum solutions to the Einstein equations, hereafter referred to as linearized multipole solution (LM). We…
Vacuum cosmological models are considered in the context of a multidimensional theory of gravity with integrable Weyl geometry. A family of exact solutions with a chain of internal spaces is obtained. Models with one internal space are…
We present analytical solutions describing a family of both inwardly and outwardly spiralling orbits in the Kerr spacetime. The solutions are exact, and remarkable for their simplicity. These orbits all have the angular momentum and energy…
The study investigates orbital motion of test particles near compact objects described by solutions involving massless scalar fields, electromagnetic fields, and nonlinear electrodynamics. Specifically, we analyze orbital dynamics in the…
Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…