Lorentzian wormhole solutions are investigated in the context of the $D$-dimensional Einstein-Gauss-Bonnet theory of gravitation. These wormholes are found to have features depending on the dimensionality of the spacetime and the coupling coefficient $\alpha$ of the Gauss-Bonnet combination. In a large number of cases, the wormhole throat radius is constrained to have a value greater than a certain number depending on $D$ and $\alpha$. The possibility of obtaining solutions with normal and exotic matter limited to the vicinity of the throat is explored. Similar to the situation in general relativity, the violation of the weak energy condition persists for $\alpha >0\mathrm{}$. For $\alpha <0\mathrm{}$, this condition may or may not be violated depending on the nature of an inequality involving $\left|\alpha \right|$, $D$, the radius $r$, and the wormhole shape function $b\left(r\right)\mathrm{}$.

• Received 7 February 1992

DOI:https://doi.org/10.1103/PhysRevD.46.2464