Figure 30

Figure 30: “Small wave fronts” of the light cone in the spacetime (156View Equation) of a plane gravitational wave. The picture shows the intersection of the light cone of Figure 29 with the lightlike hyperplane u = constant for three different values of the constant: (a) exactly at the caustic (parabola), (b) at a larger value of u (hyperbolic paraboloid), and (c) at a smaller value of u (elliptic paraboloid). In each case, the hyperplane u = constant does not intersect the one generator c tangent to @v; all other generators are intersected transversely and exactly once.