Intra--Galactic thin shell wormhole and its stability

In this paper, we construct an intra-galactic thin shell wormhole joining two copies of identical galactic space times described by the Mannheim-Kazanas de Sitter solution in conformal gravity and study its stability under spherical perturbations. We assume the thin shell material as a Chaplygin gas and discuss in detail the values of the relevant parameters under which the wormhole is stable. We study the stability following the method by Eiroa and we also qualitatively analyze the dynamics through the method of Weierstrass. We find that the wormhole is generally unstable but there is a small interval in radius for which the wormhole is stable.