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 nonminimal 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 behavior of the bound states trapped in the potential wells and provide the flow between the two AdS regions.