Vacuum Traversable Wormhole

Abstract

We present an exact axially symmetric traversable wormhole of Einstein'sfield equations in vacuum. This solution is a geometrically modified versionof the \textit{Yilmaz} \textit{exponential metric} which has recently beenshown to represent a traversable wormhole. This vacuum wormhole is aone-parameter static singular solution with its singularity placed at $r=0$.The throat is located at $r\simeq 0.5M$ in which $M$ is the total mass ofthe wormhole. In analogy with the exponential wormhole, we show that thismodified exponential wormhole satisfies the flare-out conditions.Furthermore, it is shown that the circular stable orbit doesn't exist for anull particle, however, for a massive particle such exists provided theradius of the circular orbit is larger than a minimum radius. This is inanalogy with the Schwarzschild as well as the exponential metric.

Keywords: Wormhole, Exponential metric, Vacuum solution, Exact solution