Wave Fronts in a Causality-Violating Gödel-Type Metric

Figure 3

A plot of the spatial path of a light ray in the plane in the Gödel metric. The light ray is emitted from and travels counterclockwise. According to an observer at the origin, when the light ray has reached by moving directly from the initial point, a blue sky pair of pulses begins at . Part of this pulse travels back towards the original pulse and annihilates at with the initial pulse, when the forward moving pulse is at . Both the annihilation and blue sky positions are hidden from the observer at the origin due to the circle that delineates the causally connected region.