Figure 25: Past light cone of an
event in the spacetime
of a transparent string of finite radius with and . The metric (133)
is matched at to an
interior metric, and light rays are
allowed to pass through the interior region. The perspective is
analogous to Figure 24. The light rays which
were blocked by the string in the non-transparent case now form a
caustic. In the (2+1)-dimensional
picture the caustic consists of two lightlike curves that meet in a
swallow-tail point (see
Figure 26 for a close-up). Taking the -dimension into account, the
caustic actually consists of two
lightlike 2-manifolds (fold surfaces) that meet in a spacelike
curve (cusp ridge). The third picture in Figure 2 shows
the situation projected to 3-space. Each of the past-oriented
lightlike geodesics that form the
caustic first passes through the cut locus (transverse
self-intersection), then smoothly slips over one of the fold surfaces. The fold surfaces
are inside the chronological past , the cusp ridge is on its boundary.
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