Note on linearized stability of Schwarzschild thin-shell wormholes with variable equations of state

Abstract

We discuss how the assumption of variable equation of state (EoS) allows the elimination of the instability at equilibrium throat radius a0 = 3M featured by previous Schwarzschild thin-shell wormhole models. Unobstructed stability regions are found for three choices of variable EoS. Two of these EoS entail linear stability at every equilibrium radius. Particularly, the thin-shell remains stable as a0 approaches the Schwarzschild radius 2M . A perturbative analysis of the wormhole equation of motion is carried out in the case of variable Chaplygin EoS. The squared proper angular frequency ω 2 0 of small throat oscillations is linked with the second derivative of the thin-shell potential. In various situations ω 2 0 remains positive and bounded in the limit a0 → 2M .PACS indexing codes: 04.20.Jb Complementary aspects of thick shells and thin shells appear in the sequential development of analytical gravastar models. Mazur and Mottola [7] argued for the thermodynamic stability of a gravastar model involving a (relatively thin) finite-thickness shell bounded by two thin shells. Visser and Wiltshire [8] considered the dynamical stability of a thin-shell gravastar retaining most of the original features of Mazur and Mottola's model. Chirenti and Rezzola [9] studied the stability of a spherical thick-shell gravastar model submitted to axial perturbations. The analysis of non-radial gravastar perturbations was extended by Pani et al. [10], who combined standard perturbation theory with Israel's formalism to describe polar perturbations of non-rotating, thin-shell gravastar models.The interplay of thick shells and thin shells emerges in other dynamical contexts as well. Garfinkle and Gregory [11] expanded the equations of a thick gravitating wall in powers of the thickness of the wall. They found that the zeroth-order equations reproduce the thin-wall approximation for domain walls provided by the Israel formalism. Also, they used the first-order thick-wall equations to modify thin-wall equations and discuss the motion of domain walls. Khakshournia and Mansouri [12] determined that the zeroth-order approximation of the equations of motion of a spherical dustlike thick shell coincide with equations arising from the thin-shell formalism. They also found that the effect of thickness is to speed up the collapse of the shell. More recently, Drobov and Tegai [13] added anisotropy to a thick wall of fluid and obtained the appropriate thin-shell limit.Garcia et al. (GLV) [14] have summarized the status of the energy conditions of standard general relativity in connection with the theoretical construction of wormholes. These hypothetical tunnels in spacetime are supported by "exotic matter" which violates all the pointwise and all the averaged energy conditions. To minimize the extent of this problem, researchers have considered truncated Morris-Thorne models featuring a cut-off of the stress-energy, and a junction interface. (See, for example, [15,16].) This junction constitutes a thin-shell or a boundary surface depending on ...

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

“…An EoS is an equation that relates the energy density σ and the pressure p of the throat. Of the EoSs which have been appeared in the literature, one may enumerates the barotropic EoS [22], the EoS of a (generalized) Chaplygin gas [24], polytropic gas EoS [25], phantomlike EoS and the variable EoS [5]. Nonetheless, the barotropic EoS, mathematically given by p = p (σ), due to its simple, still realistic nature, provides a useful model for the fluid's behavior on the throat of the TSW.…”

“…However, Visser's so called cut-and-paste procedure allows us to confine such a notorious matter on a very limited part of the space, the TSW itself. Moreover, the cut-and-paste procedure has the advantage that can be applied to a vast variety of spacetimes [4][5][6][7][8][9][10][11][12][13][14][15][16], while before Visser only some certain spacetimes had the structure of a wormhole [17]. It is also worth mentioning that while TSWs are categorized as traversable wormholes, not all the wormholes are considered to be traversable [18].…”

“…Once we identify this fact we present a recipe to eliminate such type of divergences. That comes by considering a more general EoS (introduced under the name "variable EoS" [4,5]), in which the pressure depends explicitly also on the radius of the shell. With the new EoS, the speed of sound relation takes the form β 2 0 = (p 0 + γ 0 ) /σ 0 , for γ 0 = const., so that the choice p 0 + γ 0 = 0 will eliminate in the limit, the singularity for the stability diagram.…”

“…We must add that, Varela in [5] has pointed out the solution for a symmetric Schwarzschild TSW without addressing the cause for such anomaly, a general removal for other TSWs, or considering asymmetrical cases. Beside the Schwarzschild ATSW, we consider extremal Reissner-Nordström (ERN), and also the dilaton TSWs as examples to show that our method for eliminating the infinite discontinuity perfectly works.…”

Stable Dyonic Thin-Shell Wormholes in Low-Energy String Theory

“…This method was applied to construct a number of thinshell wormholes (TSW), including charged TSW [11,12], TSW with a cosmological constant [13], TSW in dilaton gravity [14], TSW from the regular Hayward black hole [15], TSW in higher-dimensional Einstein-Maxwell theory [16,17], rotating TSW [18,19], quantum corrected TSW in Bohmian quantum mechanics [20], primordial wormholes induced from Grand Unified Theories (GUTs) [21,22], canonical acoustic TSW, charged TSW with dilaton field, TSW with a Chaplygin gas, traversable wormholes in the anti-de Sitter space-time, TSW with a negative cosmological 2 Advances in High Energy Physics constant, wormholes in mimetic gravity, TSW from charged black string, cylindrical TSW, and many other interesting papers , while the stability analysis is investigated by different models, for example, linear perturbations [9] and specific equations of state (EoS) such as linear barotropic gas (LBG), Chaplygin gas (CG), and logarithmic gas (LogG) for the exotic matter [14,[59][60][61][62].…”