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.