Nonlinear stability analysis of the Schwarzschild thin-shell wormholes

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 = p (σ) on the throat of the wormhole the regions of stability are independent of the explicit form of the surface energy density σ 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.

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

“…which after a substitution from (31), the latter expression becomes (37), we used the reduced form of the conservation energy relation after perturbation given by…”

“…Such investigation for the Schwarzschild TSW was performed by Poisson and Visser in [25]. Ever since, using the same formalism as [25], there have been diligent investigations on the stability of different TSWs against such a radial perturbation [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Concerning the TSW in regular spacetime, we refer to [44] where the authors investigated the mechanical stability of a TSW in the regular Hayward black hole.…”

Thin-shell wormholes with ordinary matter in pure Gauss-Bonnet gravity

“…in which v 0 is the initial velocity of the throat [58]. For weak perturbation where v 2 0 1, one may expand the potential V (a) near the equilibrium radius to write…”

Thin-shell Wormholes with Ordinary Matter in Pure Gauss-Bonnet Gravity

“…in which v 0 is the initial velocity of the throat [11]. For weak perturbation where v 2 0 1, one may expand the potential V (a) near the equilibrium radius to write…”

“…, in m-order pure Lovelock gravity [8], except for c 0 , all c k for k = m are zero and c k=m = 0. With the same line element as (6), the field equation of the m-order pure Lovelock gravity becomes c0 + cm ψ m = µ r N −1 (11) where the general solution for ψ is obtained to be…”