Caustics in general relativity

The first-order WKB approximation to solutions of Einstein's equations near a conjugate point (with respect to a fixed space-like surface) is studied. It is found that the metric can be expressed in terms of a generalized Airy function. The geometric meaning of the approximate solution is discussed and it is shown that it is completely characterized by the shear of the two null hyper-surfaces defined at a conjugate point. Applications to the question of gravitational energy flux at a conjugate point are pointed out. (author)