Study of thin-shell around wormhole

This paper explores the geometrical structure of thin-shell developed from the matching of interior traversable wormhole geometry with exterior regular black hole (Bardeen and Hayward black holes) using cut and paste technique. The surface energy density and pressure of matter distribution located at thin-shell are determined through Israel formalism that violate the null energy condition implying the existence of exotic matter at the shell. The surface stresses explain the expansion as well as collapsing nature of thin-shell. We also investigate stability of thin-shell using radial perturbation as well as linear equation of state with different choices of the shape function, i.e., b(a) = Ar-alpha + (1 - A). It is concluded that stable and unstable characteristics of thin-shell depend on the choice of the shape function.