The Gödel universe: Exact geometrical optics and analytical investigations on motion

In this work we derive the analytical solution of the geodesic equations of G\"odel's universe for both particles and light in a special set of coordinates, which reveals the physical properties of this spacetime in a very transparent way. We also recapitulate the equations of isometric transport for points and derive the solution for G\"odel's universe. The equations of isometric transport for vectors are introduced and solved. We utilize these results to transform different classes of curves along Killing vector fields. In particular, we generate nontrivial closed timelike curves from circular closed timelike curves. The results can serve as a starting point for egocentric visualizations in the G\"odel universe.

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