Highly distorted apparent horizons and the hoop conjecture

TL;DR

This paper investigates the formation and distortion of apparent horizons in high-energy collisions, providing evidence supporting the hoop conjecture and exploring the relationship between horizon topology and the conjecture.

Contribution

It demonstrates that highly distorted apparent horizons can form without violating energy conditions, supporting the hoop conjecture in four-dimensional spacetime.

Findings

Highly distorted AHs can form in pp-wave collisions.

The formation of such AHs is limited in length.

Results support the validity of the hoop conjecture.

Abstract

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.