Wormholes in higher dimensional space-time: Exact solutions and their linear stability analysis

We derive the simplest traversable wormhole solutions in $n$-dimensional general relativity, assuming static and spherically symmetric spacetime with a ghost scalar field. This is the generalization of the Ellis solution (or the so-called Morris-Thorne's traversable wormhole) into a higher-dimension. We also study their stability using linear perturbation analysis. We obtain the master equation for the perturbed gauge-invariant variable and search their eigenvalues. Our analysis shows that all higher-dimensional wormholes have an unstable mode against the perturbations with which the throat radius is changed. The instability is consistent with the earlier numerical analysis in four-dimensional solution.