Cylindrical Thin-shell Wormholes in $f(R)$ gravity

TL;DR

This paper constructs and analyzes the stability of charged black string thin-shell wormholes within $f(R)$ gravity, revealing the existence of both stable and unstable solutions depending on model parameters, and recovering general relativity results as a special case.

Contribution

It introduces a method to build thin-shell wormholes in $f(R)$ gravity and analyzes their stability, highlighting the effects of the $R+{ ext{ extdelta}} R^2$ model.

Findings

Stable and unstable solutions exist for different $ ext{ extdelta}$ values.

Results reduce to general relativity as $ ext{ extdelta} o 0$.

Stability depends on the model parameters.

Abstract

In this paper, we employ cut and paste scheme to construct thin-shell wormhole of a charged black string with $f(R)$ terms. We consider $f(R)$ model as an exotic matter source at wormhole throat. The stability of the respective solutions are analyzed under radial perturbations in the context of $R+{\delta}R^2$ model. It is concluded that both stable as well as unstable solutions do exist for different values of $\delta$. In the limit $\delta{\rightarrow}0$, all our results reduce to general relativity.