Figure 12: Past light cone in the
Schwarzschild spacetime. One sees that the light cone wraps
around the horizon, then forms a tangential
caustic. In the picture the caustic looks like a transverse
self-intersection because one spatial
dimension is suppressed. (Only the hyperplane is shown.) There is no radial caustic. If one follows
the light rays further back in time, the light cone wraps around the horizon again and again, thereby
forming infinitely many tangential caustics which alternately cover the radius line through the
observer and the radius line opposite to the observer. In
spacetime, each caustic is a spacelike curve
along which ranges from
to , whereas ranges from to some maximal value and then
back to . Equal-time
sections of this light cone are shown
in Figure 13.
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