Figure 27

Figure 27: Instantaneous wave fronts in the spacetime of a non-transparent string of finite radius $ρ∗$ with $k = 0.8$ and $a = 0$ . The picture shows in 3-dimensional space the intersections of the light cone of Figure 24 with three hypersurfaces $t = constant$ , at values $t1 > t2 > t3$ . The vertical coordinate is the $z$ -coordinate which was suppressed in Figure 24. Only one half of each instantaneous wave front is shown so that one can look into its interior. There is a transverse self-intersection (cut locus) but no caustic.