Hyperbolic, Ultrastatic Wormhole Solution to the Vacuum Effective Gravity Equations in Randall Sundrum Brane World

Abstract

We provide a traversable wormhole solution to the effective vacuum gravity equations in Randall Sundrum brane world scenario. We argue that graviton effects from the bulk spacetime can stabilize the wormhole"s throat against collapse without the need of any “exoticmatter’’ on the brane. We also construct an ultrastatic, spherically symmetric, horizon free wormnhole with spatial hyper surfaces of RxS2 topology. The components of the effective energy momentum tensor, induced by the Weyl five dimensional curvature tensor, were calculated explicitly as functions of the radial proper distance and the radius of the throat of the wormnhole.