Stability of a $d$-dimensional thin-shell wormhole surrounded by quintessence

We study the stability of different higher dimensional thin--shell wormholes (HDTSW) in general relativity with a cosmological constant. We show that a $d$--dimensional thin--shell wormhole surrounded by quintessence can have three different throat geometries: spherical, planar and hyperbolic. Unlike the spherical geometry, the planar and hyperbolic geometries allow different topologies that can be interpreted as higher-dimensional domain walls or branes connecting two universes. To construct these geometries, we use the cut-and-paste procedure by joining two identical vacuum spacetime solutions. Properties such as the null energy condition and geodesics are also studied. A linear stability analysis around the static solutions is carried out. Our stability analysis takes into account a more general HDTSW geometry than previous works so it is possible to recover other well-known stability HDTSW conditions.