Geodesics in a Toroidal space-time

Abstract

We take a three dimensional Euclidian metric in toroidal coordinates and consider the corresponding Laplace equation. The simplest solution of this equation is taken. Based on this we build a Weyl space-time. This space-time is transformed to cylindrical coordinates. It is shown by using Mathematica that Weyl equations in cylindrical coordinates are satisfied. Geodesic motion is considered along the symmetric axis as well as along the radii of the singularity, which is the cause of the space time.