Figure 24

Figure 24: Past light cone of an event pO in the spacetime of a non-transparent string of finite radius r* with k = 0.8 and a = 0. The metric (133View Equation) is considered on the region r > r*, and the light rays are cut if they meet the boundary of this region. The z coordinate is not shown, the vertical coordinate is time t. The “chimney” indicates the region r < r* which is occupied by the string. The light cone has no caustic but a transverse self-intersection (cut locus). The cut locus, in the (2+1)-dimensional picture represented as a curve, is actually a 2-dimensional spacelike submanifold. When passing through the cut locus, the lightlike geodesics leave the boundary of the chronological past I- (pO). Note that the light cone is not a closed subset of the spacetime.