We argue that one can nucleate a traversable wormhole via a nonperturbative process in quantum gravity. To support this, we construct spacetimes in which there are instantons giving a finite probability for a test cosmic string to break and produce two particles on its ends. One should be able to replace the particles with small black holes with only small changes to the spacetime away from the horizons. The black holes are then created with their horizons identified, so this is an example of nucleating a wormhole. Unlike previous examples where the created black holes accelerate apart, in our case they remain essentially at rest. This is important since wormholes become harder and harder to make traversable as their mouths become widely separated, and since traversability can be destroyed by Unruh radiation. In our case, back-reaction from quantum fields can make the wormhole traversable.

Despite the recent evidence that anti-de Sitter (AdS) spacetime is nonlinearly unstable, we argue that many asymptotically AdS solutions are nonlinearly stable. This includes geons, boson stars and black holes. As part of our argument, we calculate the frequencies of long-lived gravitational quasinormal modes of AdS black holes in various dimensions. We also discuss a new class of asymptotically AdS solutions describing noncoalescing black hole binaries. © 2012 IOP Publishing Ltd.