Related papers: Generalized geodesic deviation in de Sitter spacet…
We develop a generic spacetime model in General Relativity which can be used to build any gravitational model within General Relativity. The generic model uses two types of assumptions: (a) Geometric assumptions additional to the inherent…
Newton's second law: "force = time-derivative of momentum", may also be defined for theories of gravitation endowing space-time with a curved metric. Thus, Einstein's assumption of a geodesic motion may be rewritten in that form, and it…
We present the explicit solution to the geodesic equations in a warped de Sitter space-time proposed by Randall-Sundrum. We find that a test particle moves in the bulk and is not restricted on a 3-brane (to be taken as our universe). On the…
The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
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…
In the context of metric $f(R)$ gravity, the Geodesic Deviation Equation (GDE) was first studied in arXiv:1010.5279v3, giving a general expression and studying a particular case, the FLRW universe. In the paper arXiv:1312.2022v1 a similar…
The relative geodesic motion on $(1+3)$-dimensional anti-de Sitter spacetimes is studied in terms of conserved quantities by adapting the Nachtmann boosting method created initially for the de Sitter spacetimes. In this approach the…
We establish an in-in formalism for geodesic deviation as an alternative to Synge calculus, based on a covariant calculus of differential forms in tangent bundle. This derives the exact Lagrangian and equations governing the finite geodesic…
We introduce and develop the concepts of Geometric Backward Stochastic Differential Equations (GBSDEs, for short) and two-driver BSDEs. We demonstrate their natural suitability for modeling continuous-time dynamic return risk measures. We…
Oscillatons are spherically symmetric solutions to the Einstein Klein Gordon (EKG) equations for soliton stars made of real time dependent scalar fields. These equations are non singular and satisfy flatness conditions asymptotically with…
General Relativity is known to produce singularities in the potential generated by a point source. Our universe can be modelled as a de Sitter (dS) metric and we show that ghost-free Infinite Derivative Gravity (IDG) produces a non-singular…
In this paper we construct a discrete simulation of an expanding homogeneous and isotropic space-time that expands via expansion of its basic elements to figure out properties and characteristics of such a space-time and derive conclusions.…
Modified gravity theories on cosmic scales have three key deviations from general relativity. They can cause cosmic acceleration without a physical, highly negative pressure fluid, can cause a gravitational slip between the two metric…
The theory of geodesic regression aims to find a geodesic curve which is an optimal fit to a given set of data. In this article we restrict ourselves to the Riemannian manifold of positive definite operators (matrices) on a Hilbert space of…
We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of…
Circular and radial geodesics are studied in the spacetime described by the $\gamma$ metric. Their behaviour is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical…
The problem of a rigorous theory of singularities in space-times with torsion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their…
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…
In this paper, we investigate gravitational waves beyond the linear approximation, focusing on second-order contributions sourced by linearized waves in the transverse-traceless (TT) gauge. A general spacetime metric is constructed, and…