3+1 -dimensional Thin Shell Wormhole With Deformed Throat can be Supported by Normal Matter

From the physics standpoint the exotic matter problem is a major difficulty in thin shell wormholes (TSWs) with spherical/cylindrical throat topologies. We aim to circumvent this handicap by considering angle dependent throats in 3+1 dimensions. By considering the throat of the TSW to be deformed spherical, i.e., a function of θ and φ , we present general conditions which are to be satisfied by the shape of the throat in order to have the wormhole supported by matter with positive density in the static reference frame. We provide particular solutions/examples to the constraint conditions.