Figure 28

Figure 28: Instantaneous wave fronts in the spacetime of a transparent string of finite radius r* with k = 0.8 and a = 0. The picture is related to Figure 25 as Figure 27 is related to Figure 24. Instantaneous wave fronts that have passed through the string have a caustic, consisting of two cusp ridges that meet in a swallow-tail point. This caustic is stable (see Section 2.2). The caustic of the light cone in Figure 25 is the union of the caustics of its instantaneous wave fronts. It consists of two fold surfaces that meet in a cusp ridge, like in the third picture of Figure 2.