Highly distorted apparent horizons and the hoop conjecture

Understand

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.