Possible wormholes in a brane world

The condition $R=0,$ where R is the four-dimensional scalar curvature, is used for obtaining a large class (with an arbitrary function of $r)$ of static, spherically symmetric Lorentzian wormhole solutions. The wormholes are globally regular and traversable, can have throats of arbitrary size and can be both symmetric and asymmetric. These solutions may be treated as possible wormhole solutions in a brane world since they satisfy the vacuum Einstein equations on the brane where effective stress-energy is induced by interaction with the bulk gravitational field. Some particular examples are discussed.