Abstract
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=pleft( sigma right) on the throat of the wormhole the regions of stability are independent of the explicit form of the surface energy density sigma 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.
Highlights
In the linear stability analysis it is assumed that a static equilibrium radius exists where a0 = a0 = a0 = 0
Investigating the stability status of the TSW at its equilibrium point i.e., a = a0 requires a perturbation upon which the TSW becomes a dynamic system
If one assumes that the perturbation is of the form of an initial kinetic energy, its initial velocity can not be zero, i.e., a0 = 0
Summary
As we will show in this paper, assuming a very small initial velocity i.e., a02 1, the results of the linear stability analysis are verified. For a greater values for the initial velocity, it is natural to expect some modifications in the results of the linear stability. The initial values of the motion will be assumed in accordance with the kinetic energy perturbation such that a0 = v0 = 0. As we shall see in the paper, in order to find a larger picture of the motion of the STSW after the perturbation, one needs to consider an equation of state (EoS) for the fluid matter presented on the STSW. Three different barotropic EoS will be considered and the effective potential and the status of the stability for the initial equilibrium point will be investigated.
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