Thin-shell bubbles and information loss problem in anti de Sitter background

We study the motion of thin-shell bubbles and their tunneling in anti de Sitter (AdS) background. We are interested in the case when the outside of a shell is a Schwarzschild-AdS space (false vacuum) and the inside of it is an AdS space with a lower vacuum energy (true vacuum). If a collapsing true vacuum bubble is created, classically it will form a Schwarzschild-AdS black hole. However, this collapsing bubble can tunnel to a bouncing bubble that moves out to spatial infinity. Then, although the classical causal structure of a collapsing true vacuum bubble has the singularity and the event horizon, quantum mechanically the wavefunction has support for a history without any singularity nor event horizon which is mediated by the non-perturbative, quantum tunneling effect. This may be regarded an explicit example that shows the unitarity of an asymptotic observer in AdS, while a classical observer who only follows the most probable history effectively lose information due to the formation of an event horizon.