Stability and dynamics of scalar field thin-shell for renormalization group improved Schwarzschild black holes

In this paper, our main concern is to obtain the geometrical structure of a thin-shell through the match of inner flat and outer the renormalization group improved Schwarzschild black hole through a well-known cut and paste approach. Then, we are interested to discuss the dynamical configuration of thin-shell composed of a scalar field (massive and massless) through an equation of motion and Klein–Gordon’s equation. Finally, the stable configuration of thin-shell is observed through the linearized radial perturbation approach about equilibrium shell radius with a phantomlike equation of state, i.e., quintessence, dark energy, and phantom energy. It is noted that stable/unstable behavior of thin-shell is found after the expected position of the event horizon of an exterior manifold. It is concluded that the stability of a thin-shell is greater for the choice of Schwarzschild black hole as compared to the renormalized group of improved Schwarzschild black holes.