Dynamics of magnetic shells and information loss problem

We investigate dynamics of magnetic thin-shells in three dimensional anti de Sitter background. Because of the magnetic field, an oscillatory solution is possible. This oscillating shell can tunnel to a collapsing shell or a bouncing shell, where both of tunnelings induce an event horizon and a singularity. In the entire path integral, via the oscillating solution, there is a non-zero probability to maintain a trivial causal structure without a singularity. Therefore, due to the path integral, the entire wave function can conserve information. Since an oscillating shell can tunnel after a number of oscillations, in the end, it will allow an infinite number of different branchings to classical histories. This system can be a good model of the effective loss of information, where information is conserved by a solution that is originated from gauge fields.