The occurrence of chaos for test particles moving in a Taub-NUT spacetime with a dipolar halo perturbation is studied using Poincaré sections. We find that the NUT parameter (magnetic mass) attenuates the presence of chaos. PACS numbers: 04.20.Jb, 04.70.Bw, 05.45.+b. Typeset using REVTEX ∗e-mail: [email protected] †e-mail: [email protected] 1 The Taub-NUT (Newman, Tamburino and Unti) ...

Cartan’s spacetime reformulation of the Newtonian theory of gravity is a generallycovariant Galilean-relativistic limit-form of Einstein’s theory of gravity known as the Newton-Cartan theory. According to this theory, space is flat, time is absolute with instantaneous causal influences, and the degenerate ‘metric’ structure of spacetime remains fixed with two mutually orthogonal non-dynamical m...

In flat spacetime, as a simple 4-vector, a particle’s 4-velocity cannot be changed by translation. Parallel translation then produces constant velocity, motion without force. Here we consider richer representations of the Poincaré group of symmetries of flat spacetime in which direct sums of a 4-vector and a 2nd rank tensor are transformed. Translation then adds a non-linear connection term to ...

We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resulting system of Euler–Lagrange equations. In the first part of the paper we lo...

The spacetime ontology is considered in General Relativity (GR) in view of the choice of a frame of reference (FR). Various approaches to a description of the FR, such as coordinate systems, monads and tetrads are reviewed. It is shown that any of the existing FR definitions require a preexisting background spacetime, which, if defined independently of the FR, renders the spacetime absolute in ...

In this note we have considered a relativistic Nambu-Goto model for a particle in AdS metric. With appropriate gauge choice to fix the reparameterization invariance, we recover the previously discussed [7] " Exotic Oscillator ". The Snyder algebra and subsequently the κ-Minkowski spacetime are also derived. Lastly we comment on the impossibility of constructing a noncom-mutative spacetime in th...

In this note we have considered a relativistic Nambu-Goto model for a particle in AdS metric. With appropriate gauge choice to fix the reparameterization invariance, we recover the previously discussed [7] " Exotic Oscillator ". The Snyder algebra and subsequently the κ-Minkowski spacetime are also derived. Lastly we comment on the impossibility of constructing a noncom-mutative spacetime in th...