Christos Mantoulidis and Richard Schoen gave a complete characterization of all non-degenerate outermost apparent horizons and showed that its Bartnik mass coincides with the Hawking mass. These characterizations disprove a conjecture due to Gibbons in the spirit of Thorne’s hoop conjecture, and construct a new large class of examples of horizons with arbitrarily negative integral curvature.

 

Reference: arXiv: 1412.0382v2.