Related papers: Godel spacetime: elliptic-like geodesics and gyros…
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…
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…
We investigate the geodesic motions of a massive particle and light ray in the hyperplane orthogonal to the symmetry axis in the 5-dimensional hypercylindrical spacetime. The class of the solutions depends on one constant a which is the…
A novel approximation method in studying the perihelion precession and planetary orbits in general relativity is to use geodesic deviation equations of first and high-orders, proposed by Kerner et.al. Using higher-order geodesic deviation…
Geodesics are studied in one of the Weyl metrics, referred to as the M--Q solution. First, arguments are provided, supporting our belief that this space--time is the more suitable (among the known solutions of the Weyl family) for…
Apsidal motion is the precession of the line of apsides in the orbit of a binary star due to perturbations from General Relativity (GR), tides, or third-body interactions. The rate of precession due to tidal effects depends on the interior…
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a General Relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this…
The precession angular velocity of a gyroscope moving along a general geodesic in the Kerr spacetime is analyzed using the geometric properties of the spacetime. Natural frames along the gyroscope world line are explicitly constructed by…
The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the…
We review the derivation of the metric for a spinning body of any shape and composition using linearized general relativity theory, and also obtain the same metric using a transformation argument. The latter derivation makes it clear that…
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…
General relativistic spin-orbit interaction leads to the quasiresonant oscillation of the gyroscope mass center along the orbital normal. The beating amplitude does not include the speed of light and equals the ratio of the intrinsic…
This paper performs a systematic investigation of geodesic motion in Euclidean Schwarzschild geometry, which is studied in the equatorial plane. The explicit form of geodesic motion is obtained in terms of incomplete elliptic integrals of…
We present a family of analytic solutions for the nearly-equatorial motion of a test particle with precessing spin in Kerr spacetime. We solve the equations of motion up to linear order in the small body's spin for periodic and homoclinic…
In this paper, we study the geodesic motion in the spacetime of a SU(2)-colored (A)dS black hole in conformal gravity, and also we investigate spacetime features, such as light spheres and horizons. Moreover, we derive the analytical…
In this article we study the geodesic motion of test particles and light in the five-dimensional Myers-Perry-anti de Sitter spacetime. We derive the equations of motion and present their solutions in terms of the Weierstra{\ss} $\wp$-,…
Exact plane gravitational radiation fields are presented within the framework of general relativity and their properties are described. The physics of nonlinear elliptically polarized plane gravitational waves is developed in close analogy…
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…
The geometry around a rotating massive body, which carries charge and electrical currents, could be described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). When a small body is…
The advanced state of cosmological observations constantly tests the alternative theories of gravity that originate from Einstein's theory. However, this is not restricted to modifications to general relativity. In this sense, we work in…