Dilaton thin-shell wormholes supported by a generalized Chaplygin gas

In this article, we construct spherical thin-shell wormholes with charge in dilaton gravity. The exotic matter required for the construction is provided by a generalized Chaplygin gas. We study the stability under perturbations preserving the symmetry. We find that the increase of the coupling between the dilaton and the electromagnetic fields reduces the range of the parameters for which stable configurations are possible.

Figure 1

Dilaton wormholes with $b=0.1$ supported by a generalized Chaplygin gas with $\alpha =0.2$: the dashed curves represent the unstable static solutions with throat radius $a_0$ for given parameters $A$, $M$ and $Q$; there are not stable static solutions. The darker (lighter) gray zones are unphysical, corresponding to a throat radius smaller than the horizon (singularity) radius of the original manifold. The event horizon and the naked singularity match for a critical value of charge $|Q_c|/M=(1+b^2{)}^{1/2}$ and the geometry is not well defined for $|Q|/M>|Q_m|/M=(1-b^2{)}^{-1/2}$.

Figure 2

Dilaton wormholes with $b=0.1$ supported by a generalized Chaplygin gas with $\alpha =0.6$: the dashed curves represent the unstable static solutions with throat radius $a_0$ for given parameters $A$, $M$ and $Q$; the solid curves represent the stable static solutions. The meaning of the gray zones and the charges $Q_c$ and $Q_m$ are explained in Fig. 1.

Figure 3

Dilaton wormholes with $b=0.1$ supported by a generalized Chaplygin gas with $\alpha =1$: the dashed curves represent the unstable static solutions with throat radius $a_0$ for given parameters $A$, $M$ and $Q$; the solid curve represent the stable static solutions. The meaning of the gray zones and the charges $Q_c$ and $Q_m$ are explained in Fig. 1. Note that the horizontal scale has changed.

Figure 4

Dilaton wormholes with $b=0.5$ supported by a generalized Chaplygin gas with $\alpha =0.2$: the dashed curves represent the unstable static solutions with throat radius $a_0$ for given parameters $A$, $M$ and $Q$; there are not stable static solutions. The meaning of the gray zones and the charges $Q_c$ and $Q_m$ are explained in Fig. 1.

Figure 5

Dilaton wormholes with $b=0.5$ supported by a generalized Chaplygin gas with $\alpha =0.6$: the dashed curves represent the unstable static solutions with throat radius $a_0$ for given parameters $A$, $M$ and $Q$; there are not stable static solutions. The meaning of the gray zones and the charges $Q_c$ and $Q_m$ are explained in Fig. 1.

Figure 6

Dilaton wormholes with $b=0.5$ supported by a generalized Chaplygin gas with $\alpha =1$: the dashed curves represent the unstable static solutions with throat radius $a_0$ for given parameters $A$, $M$ and $Q$; the solid curve represent the stable static solutions (see the magnified region). The meaning of the gray zones and the charges $Q_c$ and $Q_m$ are explained in Fig. 1. Note that the horizontal scale has changed.