Related papers: Note on equatorial geodesics in circular spacetime…
In this paper, the equations of motion for geodesics in the neutral rotating Black Ring metric are derived and the separability of these equations is considered. The bulk of the paper is concerned with sets of solutions where the geodesic…
In this paper, Clairaut's theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
We prescribe a pseudo-Newtonian vector potential for studying accretion disks around Kerr black holes. The potential is useful to study the inner properties of disk not confined to the equatorial plane where general relativistic effect is…
We make some remarks on the existence of a geodesically complete core for any compact non-positively curved space.
The Kerr-star spacetime is the extension over the horizons and in the negative radial region of the slowly rotating Kerr black hole. It is known that below the inner horizon, there exist both timelike and null (lightlike) closed curves.…
Closed optical trajectories in Kerr spacetime are engineered to exhibit a marked lack of symmetry. The eccentricity manifests as a holonomy in gravitational Faraday rotation that can be made arbitrarily large by radial translation of the…
The spacetime geometry on the equatorial slice through a Kerr black hole is formally equivalent to the geometry felt by phonons entrained in a rotating fluid vortex. We analyse this situation in some detail: First, we find the most general…
An exact solution of Einstein's field equations in empty space first found in 1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes Kerr spacetime to include the case of matter with arbitrary mass quadrupole moment…
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…
In this paper we present a new public code, named $ynogkm$, for the fast calculation of time-like geodesics in the Kerr-Newmann (K-N) spacetime, which is a direct extension of $ynogk$ calculating null geodesics in a Kerr spacetime.…
Karlsson and Margulis proved in the setting of uniformly convex geodesic spaces, which additionally satisfy a nonpositive curvature condition, an ergodic theorem that focuses on the asymptotic behavior of integrable cocycles of nonexpansive…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
The quasilocal energy associated with a constant stationary time slice of the Kerr spacetime is presented. The calculations are based on a recent proposal \cite{by} in which quasilocal energy is derived from the Hamiltonian of spatially…
We define the notion of geodesic completeness for semi-Riemannian metrics of low regularity in the framework of the geometric theory of generalized functions. We then show completeness of a wide class of impulsive gravitational wave…
We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass…
Rotation of polarization in an external gravitational field is one of the effects of general relativity that can serve as a basis for its precision tests. A careful analysis of reference frames is crucial for a proper evaluation of this…
We review the analytical solution methods for the geodesic equations in Kerr-Newman-Taub-NUT-de Sitter spacetimes and its subclasses in terms of elliptic and hyperelliptic functions. A short guide to corresponding literature for general…
For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all…
The geodesic total curvature of rectifiable spherical curves is analyzed. We extend to the case of high dimension spheres the explicit formula that holds true for curves supported into the 2-sphere. For this purpose, we take advantage of…