  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.
