Related papers: Generalized geodesic deviation in de Sitter spacet…
The idea that the quantum space-time of microphysics may be fractal everywhere was intensively investigated recently, and several authors have presented the geodesic equations of different fractal space - times. In the present work we…
The time dependent conformally-flat spherical Rindler spacetime is investigated. The geometry has an apparent horizon that coincides with the causal horizon. The scalar acceleration of a static observer is constant and equals to the…
Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without linear structure. In such settings the classical additive error…
In this note we reduce the problem of geodesic connectedness in a wide class of G\"odel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
The deflection and gravitational lensing of light and massive particles in arbitrary static, spherically symmetric and asymptotically (anti-)de Sitter spacetimes are considered in this work. We first proved that for spacetimes whose metric…
The construction of an averaged theory of gravity based on Einstein's General Relativity is very difficult due to the non-linear nature of the gravitational field equations. This problem is further exacerbated by the difficulty in defining…
In this essay we propose that the theory of gravity's vacuum is described by a de Sitter geometry. Under this assumption we consider an adjustment mechanism able to screen any value of the vacuum energy of the matter fields. We discuss the…
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of G\"{o}del-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the…
We consider f(R,T) modified theory of gravity in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We indicate that in this type of the theory,…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of…
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…
We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For…
A duality between spacetime manifolds, the geodesic duality, is introduced. Two manifolds are geodesic dual, if the transformation between their metrics is also the transformation between their geodesics. That is, the transformation that…
The de Sitter invariant special relativity is a natural extension of the usual Einstein special relativity. Within this framework a generalization of special relativity (SR) for the de Sitter space-time introduces a new length scale $R$,…
We shall here discuss a characterization of geodesics trajectories. We shall show that the action of the gravitational field on mass particles can be essentially identified with the force that cannot be absolutely eliminated. This leads to…
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat…
We exploit an interpretation of gravity as the symmetry broken phase of a de Sitter gauge theory to construct new solutions to the first order field equations. The new solutions are constructed by performing large $Spin(4,1)$ gauge…
Referring to the behavior of accelerating objects in special relativity, and applying the principle of equivalence, one expects that the coordinate acceleration of point masses under gravity will be velocity dependent. Then, using the…