Gravitational instability of exotic compact objects

Exotic compact objects with physical surfaces a Planckian distance away from where the horizon would have been are inspired by quantum gravity. Most of these objects are defined by a classical spacetime metric, such as boson stars, gravastars and wormholes. We show that these classical objects are gravitationally unstable because accretion by ordinary and dark matter, and by gravitational waves, forces them to collapse into a black hole by the Hoop conjecture. To avoid collapse, either their surface must be a macroscopic distance away from the horizon, or they must violate the null energy condition.