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 space-time 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 the four-dimensional solution.