Sculpting Spacetime: Thin Shells in Wormhole Physics

In this work, we employ the Darmois-Israel thin-shell formalism to construct both static and dynamic thin-shell configurations surrounding traversable wormholes. Initially, using the cut-and-paste technique, we perform a linearized stability analysis in the presence of a general cosmological constant. Our results show that for sufficiently large positive values of the cosmological constant, corresponding to the Schwarzschild-de Sitter geometry, the stability regions of the wormhole solutions are significantly enhanced compared to the Schwarzschild case. Subsequently, we construct static thin-shell solutions by matching an interior wormhole geometry to an exterior vacuum spacetime across a junction surface. In the spirit of minimizing the presence of exotic matter, we identify parameter domains in which the null and weak energy conditions are satisfied at the shell. We examine the surface stress-energy components in detail, determining regions where the tangential surface pressure is either positive or negative, interpreted, respectively, as the pressure or surface tension. Additionally, an expression describing the behavior of the radial pressure across the junction is derived. Finally, we determine key geometrical characteristics of the wormhole, including the throat radius and the junction interface radius, by imposing traversability conditions. Estimates for the traversal time and required velocity are also provided, further elucidating the physical viability of these configurations.