Nonlinear stability analysis of the Schwarzschild thin-shell wormholes

Eric Poisson and Matt Vissert in their 1995 paper studied the linear stability of the Schwarzschild thin-shell wormholes (STSW). It was shown that for a generic equation of state (EoS) of the form p=pσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=p\left( \sigma \right) $$\end{document} on the throat of the wormhole the regions of stability are independent of the explicit form of the surface energy density σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} and the EoS. Here in this work, the nonlinear version of their stability analysis is presented. To do so, three specific EoSs namely a linear, a quadratic and a power law barotropic EoS are considered. For every EoSs, the analytic function of the effective potential is obtained. Finally, the possible motions of the STSW within the corresponding effective potentials are studied.