Related papers: Generalized geodesic deviation in de Sitter spacet…
We investigate the geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional form of the metric. Employing a 5-dimensional embedding formalism and a…
We show that the acceleration-difference of neighboring free-falling particles (= geodesic deviation) measured in the local reference frame of a GR-noninertial observer is not given by the Riemann tensor. With the gravito-electric field of…
In this paper, we give a rigorous derivation of Einstein's geodesic hypothesis in general relativity. We use scaling stable solitons for nonlinear wave equations to approximate the test particle. Given a vacuum spacetime $([0,…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
We formulate geodesics on a manifold in terms of a parallel transfer of a particle state vector transformed by local Lorentz and Yang-Mills symmetry groups. This formulation leads to an introduction of a canonical one-form the eigenvalues…
The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at…
The relative motion of many particles can be described by the geodesic deviation equation. This can be derived from the second covariant variation of the point particle's action. It is shown that the second covariant variation of the string…
The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is…
We propose an action for a free particle in Horava-Lifshitz gravity based on Foliation Preserving Diffeomorphisms. The action reduces to the usual relativistic action in the low energy limit and allows for subluminal and superluminal…
With appropriately chosen parameters, the C-metric represents two uniformly accelerated black holes moving in the opposite directions on the axis of the axial symmetry (the z-axis). The acceleration is caused by nodal singularities located…
We show that the path of any accelerated body in an arbitrary space-time geometry $g_{\mu\nu}$ can be described as geodesics in a dragged metric $\hat{q}_{\mu\nu}$ that depends only on the background metric and on the motion of the body.…
We analyze the behavior of causal geodesics on a Kerr-de Sitter spacetime with particular emphasis on their completeness property. We set up an initial value problem (IVP) whose solutions lead to a global understanding of causal geodesics…
The motion of sufficiently small body in general relativity should be accurately described by a geodesic. However, there should be ``gravitational self-force'' corrections to geodesic motion, analogous to the ``radiation reaction forces''…
We study singularities of geodesics flows in two-dimensional generalized Finsler spaces (pseudo-Finsler spaces). Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of…
A region-delimited gravitational wave field can be constructed, such that a subset of geodesics crossing this region will move faster than nearby geodesics moving entirely inside flat spacetime, along a preferred direction. Null geodesics…
Several space missions such as GRACE, GRAIL, ACES and others rely on intersatellite communications (ISC) between two satellites at a large distance one from another. The main goal of the theory is to formulate all the navigation observables…
A positive mass theorem for General Relativity Theory is proved. The proof is 4-dimensional in nature, and relies completely on arguments pertaining to causal structure, the basic idea being that positive energy-density focuses null…
Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum…
We study geodesics along a noncompact Kerr-Newman instanton, where the asymptotic geometry is either de Sitter or anti-de Sitter. We use first integrals for the Hamilton-Jacobi equation to characterize trajectories both near and away from…