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

TL;DR

This paper investigates the stability of Schwarzschild-$f(R)$ gravity thin-shell wormholes, demonstrating that stability can be achieved by matching $f(R)$-gravity wormholes with Schwarzschild vacuum using new geometric constraints.

Contribution

It introduces a method to stabilize $f(R)$-gravity wormholes by applying thin-shell junction conditions with Schwarzschild spacetime, expanding the understanding of wormhole stability.

Findings

Stability regions identified for thin-shell wormholes in $f(R)$-gravity

Application of new geometric constraints to analyze stability

Demonstration that stability is possible with Schwarzschild matching

Abstract

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.