Asymptotically anti–de Sitter cylindrical thin-shell wormholes

In this article we investigate cylindrical thin-shell wormholes which are asymptotically anti-de Sitter. We analyze their stability under perturbations preserving the symmetry by using two different methods. We compare the results with those corresponding to the wormholes constructed from the Levi-Civita spacetime. We find that the configurations always require the presence of exotic matter at the throat, and, in the case of the linearized stability analysis, they can be stable for suitable values of the parameters.

Figure 1

Thin-shell wormholes constructed from the Linet–Tian metric with $\mathrm{\Lambda }<0$: linearized stability regions (in gray) in the plane $({\eta }_1,{\eta }_2)$, for $k=0.1$ and several values of $a_0\sqrt{|\mathrm{\Lambda }|}$.

Figure 2

Thin-shell wormholes constructed from the Linet–Tian metric with $\mathrm{\Lambda }<0$: linearized stability regions (in gray) in the plane $({\eta }_1,{\eta }_2)$, for $k=0.4$ and several values of $a_0\sqrt{|\mathrm{\Lambda }|}$.

Figure 3

Thin-shell wormholes constructed from the Levi-Civita metric ($\mathrm{\Lambda }=0$): linearized stability regions (in gray) in the plane $({\eta }_1,{\eta }_2)$, for $k=0.1$ (left) and for $k=0.4$ (right). The results do not depend on $a_0$ (see text).