Stability of thin-shell-wormhole in Robertson-Walker closed universe I: static universe

Abstract

We construct a generic thin-shell wormhole (TSW) in the Robertson-Walker
(RW) cosmological model of the universe. The general formalism is presented
and here in this paper - the first part of the research- we investigate the
stability of the TSW constructed in the static RW universe. To do so, we
perform two different stability analyses namely a mechanical linear radial
perturbation and a small speed exact (not linearized) perturbation. It is
shown that the corresponding TSW is stable against a linear radial
perturbation provided that the variable equation of state of the surface
energy-momentum tensor is finely tuned. On the other hand, the exact
stability analysis in the context of small-speed perturbation reveals that
the throat of the TSW for the closed static universe oscillates between the
center of the universe and the outer boundary.