Stability of Schwarzschild-$f(R)$ gravity thin-shell wormholes

Mazharimousavi and Halilsoy [1] recently proposed wormhole solutions in $f(R)$-gravity that satisfy energy conditions but are unstable. We show here that stability could still be achieved for thin-shell wormholes obtained by gluing the wormholes in $f(R)$-gravity with the exterior Schwarzschild vacuum. Using the new geometrical constraints from thin-shell "mass" and from external "force" developed by Garcia, Lobo and Visser, we demarcate and analyze the stability regions.