Discontinuity problem in the linear stability analysis of thin-shell wormholes

Abstract

We investigate the infinite discontinuity points of stability diagram in thin-shell wormholes. The square of the speed of sound β 2 0 , which is expressed in terms of pressure and energy density at equilibrium on the throat, arises with a divergent amplitude. As this is physically non-acceptable, we revise the equation of state, such that by fine-tuning of the pressure at static equilibrium, which is at our disposal, eliminates such a singularity. The efficacy of the method is shown in Schwarzschild, extremal Reissner-Nordström, and dilaton thin-shell wormholes.

A Closed Universe: de Sitter Cosmic Gate

“…It is known from Darmois-Israel formalism that the boundary hypersurface Σ should satisfy certain junction conditions [18]. The details of the procedure are explained in many references [19][20][21][22], so here we refrain from excessive repetition. In short, the first fundamental form (the induced metric tensor) has to be continuous across the thin-shell whereas the second fundamental form (the induced curvature tensor) is discontinuous due to the presence of matter at the shell.…”

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

“…p = p (σ). Also, the choice γ 0 = −p 0 | a=a D , in which a D is the radius of discontinuity, is picked up deliberately since it removes the discontinuity in the stability diagram of barotropic TSWs [59]. Although the discontinuity radius in the case we are studying here happens to locate behind the critical radius at x 0 = 2, setting γ 0 = −p 0 | a=a D alters the behavior of the graph.…”

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

“…p = p (σ). Also, the choice γ 0 = −p 0 | a=a D , in which a D is the radius of discontinuity, is picked up deliberately since it removes the discontinuity in the stability diagram of barotropic TSWs [13]. Although the discontinuity radius in the case we are studying here happens to locate behind the critical radius at x 0 = 2, setting γ 0 = −p 0 | a=a D alters the behavior of the graph.…”