Thin-shell wormhole with a background Kalb–Ramond field

The Kalb–Ramond (KR) field is a background tensor field that arises in string theory and violates the local Lorentz symmetry of spacetime, upon acquiring the Vacuum Expectation Value (VEV). A non-minimal coupling between the KR VEV and the Ricci tensor may give rise to a modified black hole solution. Considering two copies of such black holes, we construct a thin-shell wormhole using the ‘Cut-and-Paste’ technique. Then we investigate key physical properties of the wormhole like pressure-density profile, equation of state, the geodesic motion of test particles near the wormhole throat, and the total amount of exotic matter in the throat, and examine how these properties vary with the Lorentz-Violating (LV) parameters. We find that the wormhole model violates the null and weak energy conditions, but satisfies the strong energy condition. On top of that, the velocity of the throat radius is found considering its time evolution. Finally, we analyze its linear stability against small radial perturbations.