Figure 24: Past light cone of an
event in the spacetime
of a non-transparent string of finite radius with and . The
metric (133)
is considered on the region , and the light rays
are cut if they meet the boundary of this region. The
coordinate is not shown, the vertical coordinate is time . The “chimney” indicates the
region 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 . Note that the
light cone is not a closed subset of the
spacetime.
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