Figure 12

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 $𝜗 = π ∕2$ 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 $r$ ranges from $2m$ to $∞$ , whereas $t$ ranges from $− ∞$ to some maximal value and then back to $− ∞$ . Equal-time sections of this light cone are shown in Figure 13.