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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…
Despite the extraordinary attention that modified gravity theories have attracted over the past decade, the geodesic deviation equation in this context has not received proper formulation thus far. This equation provides an elegant way to…
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…
In this article, spatially-structured gravitational waves are investigated. Drawing upon analogies between electrodynamics and general relativity, a new gauge is found. We investigate the polarization and degrees of freedom of the resulting…
We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the…
On the basis of a "local" principle of equivalence of general relativity, we consider a navigation in a kind of "4D-ocean" involving measurements of conformally invariant physical properties only. Then, applying the Pfaff theory for PDE to…
Recent astrophysical data indicate that our universe might currently be in a de Sitter (dS) phase. The importance of dS space has been primarily ignited by the study of the inflationary model of the universe and the quantum gravity. As we…
We study the classical geodesic motions of nonzero rest mass test particles and photons in (3+1+n)- dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between the motions in the…
We show how to obtain all covariant field equations for massless particles of arbitrary integer, or half-integer, helicity in four dimensions from the quantization of the rigid particle, whose action is given by the integrated extrinsic…
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…
We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modelled as small perturbations of the background Robertson-Walker geometry. The perfect fluid matter distribution…
Within the closed universe, we obtain the amplitude and frequency of gravitational waves in the terms of discrete wave numbers, wave propagation time, and cosmological constant using the deviation equation in the first-order perturbed…
These notes address the planar gravitational wave solutions of general relativity in empty space-time, and analyze the motion of test particles in the gravitational wave field. Next we consider related solutions of the Einstein equations…
We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and…
We investigate the propagation of the gravitational waves in a cosmological background. Based on the framework of spatially covariant gravity, we derive the general quadratic action for the gravitational waves. The spatial derivatives of…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally…
This work presents an alternative approach to obtain the quantum field equations in curved spacetime, considering that sufficiently small particles follow stochastic trajectories around geodesic. Our proposal is based on a stochastic…
It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
In the context of general relativity, the geodesic deviation equation (GDE) relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics. In this paper, we consider the GDE for the generalized hybrid…