Asymmetric Thin-Shell Wormholes

Abstract: Spacetime wormholes in isotropic spacetimes are represented traditionally by embedding diagrams which were symmetric paraboloids. This mirror symmetry, however, can be broken by considering different sources on different sides of the throat. This gives rise to an asymmetric thin-shell wormhole, whose stability is studied here in the framework of the linear stability analysis. Having constructed a general formulation, using a variable equation of state and related junction conditions, the results are tested for some examples of diverse geometries such as the cosmic string, Schwarzschild, Reissner-Nordstr% \"{o}m and Minkowski spacetimes. Based on our chosen spacetimes as examples, our finding suggests that symmetry is an important factor to make a wormhole more stable. Furthermore, the parameter $\gamma $, which corresponds to the radius dependency of the pressure on the wormholes's throat, can affect the stability in a great extent.