Minimum asymptotic energy of a charged spherically symmetric thin-shell wormhole and its stability

The static spherically symmetric thin shell of proper mass $m$ and electric charge $q$ around a central star or black hole of mass $M$ is in general unstable. Although with fine-tuned $m,q,$ and $M$ it can be considered quasi-stable. These facts have been recently proved by Hod in \cite{HOD1} from which we are inspired to investigate the stability status of the throat of a spherically symmetric thin-shell wormhole (TSW) with the same proper mass and charge. Precisely, in this compact paper, we introduce the radius of stability for the throat of a static spherically symmetric charged TSW, by optimizing its energy measured by an asymptotic observer. Furthermore, we prove that at the stable equilibrium radius, the tension on the throat is zero, and a perturbation in the form of an initial kinetic energy results in an effective attractive potential such that the throat oscillates around the equilibrium point.