Related papers: Geodesic Deviation in Regge Calculus
This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter…
The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The…
In the present manuscript, I examine an intriguing relation at the classical level between general relativity and a theory where matter couples uniquely multiplicatively to geometry in the Lagrangian density. Interestingly, the…
The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate…
Geodesics in general relativity describe the behaviour of test particles in a gravitational field. In 5D Kaluza-Klein, geodesics reproduce the Lorentz force motion of particles in an electromagnetic field. This paper studies geodesic motion…
Discretization of general relativity is a promising route towards quantum gravity. Discrete geometries have a finite number of degrees of freedom and can mimic aspects of quantum geometry. However, selection of the correct discrete freedoms…
Responses to questions, comments and criticism of our recent paper "General Relativity Resolves.." are provided. It is emphasized that our model is entirely natural to describe the dynamics of an axially symmetric galaxy and that our…
The first results presented in our article are the clear definitions of both intrinsic and extrinsic discrete curvatures in terms of holonomy and plane-angle representation, a clear relation with their deficit angles, and their clear…
We investigate the fully general class of non-expanding, non-twisting and shear-free D-dimensional geometries using the invariant form of geodesic deviation equation which describes the relative motion of free test particles. We show that…
Concepts like peculiar velocity, gravitational force, and power spectrum and their interrelationships are of utmost importance in the theories of structure formation. The observational implementation of these concepts is usually based on…
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due…
We consider the possibility to use the areas of two-simplexes, instead of lengths of edges, as the dynamical variables of Regge calculus. We show that if the action of Regge calculus is varied with respect to the areas of two-simplexes, and…
General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the…
We study gravitational curvature effects in circular and radial geodesics in static, spherically symmetric space-times, using Fermi normal coordinates. We first set up these coordinates in the general case, and then use this to study…
In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves…
We argue that the geodesic rule, for global defects, is a consequence of the randomness of the values of the Goldstone field $\phi$ in each causally connected volume. As these volumes collide and coalescence, $\phi$ evolves by performing a…
How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity,…
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 show that the Equivalence Principle (EP) is violated by Quantum Gravity (QG) effects. The predicted violations are compared to experimental observations for Gravitational Redshift, Law of Reciprocal Action and Universality of Free Fall.…
For field theories in curved spacetime, defining how matter gravitates is part of the theory building process. In this letter, we adopt Bekenstein's multiple geometries approach to allow part of the matter sector to follow the geodesics on…