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

TL;DR

This paper derives higher-dimensional traversable wormhole solutions in general relativity with a ghost scalar field and analyzes their linear stability, finding that all such wormholes are linearly unstable against perturbations.

Contribution

It generalizes the Ellis wormhole solution to higher dimensions and provides a linear stability analysis for these solutions.

Findings

All higher-dimensional wormholes exhibit an unstable mode.

The instability aligns with previous four-dimensional numerical results.

Master equation for perturbations was derived and analyzed.

Abstract

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.