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We derive the simplest traversable wormhole solutions in $n$-dimensionalgeneral relativity, assuming static and spherically symmetric spacetime with aghost scalar field. This is the generalization of the Ellis solution (or theso-called Morris-Thorne's traversable wormhole) into a higher-dimension. Wealso study their stability using linear perturbation analysis. We obtain themaster equation for the perturbed gauge-invariant variable and search theireigenvalues. Our analysis shows that all higher-dimensional wormholes have anunstable mode against the perturbations with which the throat radius ischanged. The instability is consistent with the earlier numerical analysis infour-dimensional solution.

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