Asymmetric thin-shell wormholes

The European Physical Journal C, Jun 2018

Spacetime wormholes in isotropic spacetimes are represented traditionally by embedding diagrams which were symmetric paraboloids. This mirror symmetry, however, can be broken by considering different sources on different sides of the throat. This gives rise to an asymmetric thin-shell wormhole, whose stability is studied here in the framework of the linear stability analysis. Having constructed a general formulation, using a variable equation of state and related junction conditions, the results are tested for some examples of diverse geometries such as the cosmic string, Schwarzschild, Reissner–Nordström and Minkowski spacetimes. Based on our chosen spacetimes as examples, our finding suggests that symmetry is an important factor to make a wormhole more stable. Furthermore, the parameter \(\gamma \), which corresponds to the radius dependency of the pressure on the wormholes’s throat, can affect the stability in a great extent.

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Asymmetric thin-shell wormholes

Eur. Phys. J. C Asymmetric thin-shell wormholes S. Danial Forghani 0 S. Habib Mazharimousavi 0 Mustafa Halilsoy 0 0 Department of Physics, Faculty of arts and sciences, Eastern Mediterranean University , Famagusta, North Cyprus, via Mersin 10 , Turkey Spacetime wormholes in isotropic spacetimes are represented traditionally by embedding diagrams which were symmetric paraboloids. This mirror symmetry, however, can be broken by considering different sources on different sides of the throat. This gives rise to an asymmetric thin-shell wormhole, whose stability is studied here in the framework of the linear stability analysis. Having constructed a general formulation, using a variable equation of state and related junction conditions, the results are tested for some examples of diverse geometries such as the cosmic string, Schwarzschild, Reissner-Nordström and Minkowski spacetimes. Based on our chosen spacetimes as examples, our finding suggests that symmetry is an important factor to make a wormhole more stable. Furthermore, the parameter γ , which corresponds to the radius dependency of the pressure on the wormholes's throat, can affect the stability in a great extent. 1 Introduction The history of wormholes goes back to the embedding diagrams of Ludwig Flamm [1] in the newly discovered Schwarzschild metric in 1916. Later on, in 1935, Einstein and Rosen [2] in search of a geometric model for elementary particles rediscovered a wormhole as a tunnel connecting two asymptotically flat spacetimes. The minimum radius of the tunnel, now known as the throat connecting two geometries, was interpreted as the radius of an elementary particle. The idea of wormhole did not go in much popularity until Morris and Thorne [3,4] gave a detailed analysis and in certain sense initiated the modern age of wormholes as tunnels connecting two spacetimes. It was already stated by Morris and Thorne that the energy density of such an object, if it ever exists, must be negative; a notorious concept in the realm of classical physics. In quantum theory, however, rooms exist to manipulate and live along peacefully with negative energy densities. Being a classical theory, general relativity must find the remedy within its classical regime without resorting to any quantum. At this stage, an important contribution came from Visser, who found a way to confine the negative energy density zone to a very narrow band of spacetime known as the thin-shell [5,6]. The idea of thin-shell wormholes (TSWs) became as popular and interesting as the standard wormholes, verified by the large literature in that context [7–9]. For some more recent works we refer to [10– 17,46]. Let us also remark that there have been attempts to construct TSWs with total positive energy against the negative local energy density [18–25]. This has been possible only by changing the geometrical structure of the throat, namely from spherical/circular to non-spherical/non-circular geometry, depending on the dimensionality. Stability of TSW is another important issue that deserves mentioning and investigation for the survival of a wormhole (Fig. 1) [26–37]. In this paper, we introduce TSWs, that are constructed from asymmetric spacetimes in the bulk [38–40]. So far, the two spacetimes on different sides of the throat, are made from the same bulk material. Our intention is to consider different spacetimes, or at least different sources in common types of spacetimes in order to create a difference between the two sides. Naturally, the reflection symmetry about the throat in the upper and lower halves will be broken and in consequence new features are expected to arise which is the basic motivation for the present study. Note that for non-isotropic bulks, asymmetric TSWs emerge naturally. For example, we consider Reissner–Nordström (RN) spacetimes on both sides with different masses and charges in two sides of the throat; Or two cosmic string (CS) spacetimes with different deficit angles to be joined at the throat. This type of TSW, which we dub as asymmetric TSW (ATSW), has not been investigated so far. For this reason, we will be focusing on such wormholes. One may anticipate that the asymmetry of the wormhole will have an impact on particle geodesics, light lensing, and other matters. Asymmetry may act instrumental in the identification of TSWs in nature, if there exists such structures. Our next concern will be to study the stability of such ATSW and novelties that will give rise, if there are any at all. As in the previous studies, an equation of state (EoS) is introduced at the throat with pressure and density to be used as the surface energy-momentum tensor. Then, the Israel junction conditions [41–45] relate these variables within an energy equation (see Eq. 16), in which Veff (a) is an effective potential. Taking derivative of the energy equation ( 16 ) will naturally yield the equation of motion. Expansion of Veff (a) about an equilibrium radius of the throat, say (...truncated)


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S. Danial Forghani, S. Habib Mazharimousavi, Mustafa Halilsoy. Asymmetric thin-shell wormholes, The European Physical Journal C, 2018, pp. 469, Volume 78, Issue 6, DOI: 10.1140/epjc/s10052-018-5776-2