Linear stability analysis of evolving thin shell wormholes

Using ideas of cosmological perturbation theories, we make general linear stability analysis of dynamic thin-shell wormholes constructed by cutting-and-pasting two building-block spacetimes at arbitrary joining shell radius. We observed that in appropriate parameter choices, dynamical thin shell wormholes following from such a cut-and-paste procedure can be kept stable during the whole evolution process towards the final extremal point on which the joining shell radius reaches on static values. Our work forms a valuable complementarity to previous analysis basing on virtual spherical perturbations around the born-static configuration of the wormholes.