  We cut a general, static, spherically symmetric spacetime and paste its copy
to make a wormhole with a thin shell of any barotropic fluid in general
relativity. We show that the stability of the thin-shell wormhole is
characterized by a set of circular photon orbits called an (anti)photon sphere
in the original spacetime if a momentum flux passing through a throat is
prohibited. Our result will be useful to classify the stability of the thin
shell on the throat against linearized spherically symmetric perturbations.
