Note on linearized stability of Schwarzschild thin-shell wormholes with variable equations of state

We discuss how the assumption of variable equation of state (EoS) allows the elimination of the instability at equilibrium throat radius a₀=3M featured by previous Schwarzschild thin-shell wormhole models. Unobstructed stability regions are found for three choices of variable EoS. Two of these EoS entail linear stability at every equilibrium radius. Particularly, the thin shell remains stable as a₀ approaches the Schwarzschild radius $2M$. A perturbative analysis of the wormhole equation of motion is carried out in the case of variable Chaplygin EoS. The squared proper angular frequency ω₀² of small throat oscillations is linked with the second derivative of the thin-shell potential. In various situations ω₀² remains positive and bounded in the limit a₀→2M.