Highly distorted apparent horizons and the hoop conjecture

By analyzing the apparent horizon (AH) formation in the collision of two pp-waves with rectangular sources in four dimensions, we study to what extent the AH can be distorted without violating the energy conditions. It is shown that the highly distorted AH can form in this system although it cannot be arbitrarily long. The hoop conjecture is examined for the formation of such highly distorted AHs, and our result gives a strong support to the hoop conjecture. We also point out the possible relation between the AH topology theorem and the hoop conjecture.