Null geodesics and wave front singularities in the Gödel space–time

We explore wave fronts of null geodesics in the Godel metric emitted from point sources both at, and away from, the origin. For constant time wave fronts emitted by sources away from the origin, we find cusp ridges as well as blue sky metamorphoses where spatially disconnected portions of the wave front appear, connect to the main wave front, and then later break free and vanish. These blue sky metamorphoses in the constant time wave fronts highlight the non-causal features of the Godel metric. We introduce a concept of physical distance along the null geodesics, and show that for wave fronts of constant physical distance, the reorganization of the points making up the wave front leads to the removal of cusp ridges.