Stability of thin-shell wormholes via polymer black hole in loop quantum gravity

The focus of this work is to examine the dynamical behavior of thin-shell wormholes developed from the polymer black hole in loop quantum gravity. Such geometrical structure is formulated by considering the cut and paste approach to avoid the appearance of singularity as well as the position of the horizon. Then, we are interested in exploring the impact of different types of matter contents on the stable configurations of the shell using linearized radial perturbation. It is observed that the quantum term ${\Theta }_k$ possesses a marvelous role in obtaining the stability of the shell. For the choice of variable phantomlike model, we find the stability for some specific values of $n$ by applying the constraints $0<{\Theta }_k<M^2$. In the literature, many researchers find stability for some specific ranges of $n$. In the presence of ${\Theta }_k$, the thin-shell wormhole becomes stable for the variable Chaplygin gas model for all choices of $n$ as compared to phantomlike and barotropic equations of state. As ${\Theta }_k$ approaches to $M^2$, we get the maximum stable behavior for all positive values of the variable $n$ for the choice of variable Chaplygin gas model.