Formation of Bound States of scalar fields in AdS-asymptotic Wormholes

We use the Wentzel-Kramers-Brillouin (WKB) approximation to study the formation and propagation of bound states in the vicinity of a wormhole in the non-minimal derivative coupling theory of gravity. The wormhole throat connects two Anti-de Sitter spacetimes. We show that when the scalar field lies in high orbital states, the corresponding potential has potential barriers that block the passage of a classical field. We investigate the behaviour of the bound states trapped in the potential wells and provide the flow between the two AdS regions.