Related papers: Geodesic Deviation in Regge Calculus
These Lecture notes give an introduction to Regge calculus as a discrete model of General Relativity.
We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard…
The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of…
The Riemannian manifold of curves with a Sobolev metric is an important and frequently studied model in the theory of shape spaces. Various numerical approaches have been proposed to compute geodesics, but so far elude a rigorous…
Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity…
The geodesic as well as the geodesic deviation equation for impulsive gravitational waves involve highly singular products of distributions $(\theta\de$, $\theta^2\de$, $\de^2$). A solution concept for these equations based on embedding the…
We briefly review past applications of Regge calculus in classical numerical relativity, and then outline a programme for the future development of the field. We briefly describe the success of lattice gravity in constructing initial data…
Conformal gravity has been proposed as an alternative theory of gravity which can account for flat galactic rotation curves without recourse to copious quantities of dark matter. However it was shown that for the usual choice of the metric,…
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…
Some first results are presented regarding the behavior of invariant correlations in simplicial gravity, with an action containing both a bare cosmological term and a lattice higher derivative term. The determination of invariant…
In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show…
Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This…
The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables…
We discuss how the vector nature of magnetic fields, and the geometrical interpretation of gravity introduced by general relativity, lead to a special coupling between magnetism and spacetime curvature. This magneto-geometrical interaction…
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one…
The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics.…
We study the derivation of the effective equation of motion for a pointlike particle in the framework of quantum gravity. Just like the geodesic motion of a classical particle is a consequence of classical field theory coupled to general…
We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our…