Approaching the surface of an Exotic Compact Object

Many approaches to quantum gravity require replacing the traditional black hole geometry with an Exotic Compact Object (ECO), which has a large but not infinite redshift at its surface. We argue that near the ECO surface, the vacuum Einstein equations imply a metric that is chaotic, with increasingly large oscillations as we approach the surface. This behavior is analogous to the 'cosmic billiards' found in the BKL analysis of cosmology near the big bang. For the ECO, some of the potential walls of this billiards change sign to become 'cliffs', resulting in a runaway behavior where some compact directions squeeze to zero size. In string theory such squeezing yields a natural continuation to the interior geometry of fuzzballs, where compact directions collapse to create monopoles.