Chaplygin traversable wormholes

The generalized Chaplygin gas (GCG) is a candidate for the unification of dark energy and dark matter, and is parametrized by an exotic equation of state given by $p_{\mathrm{ch}}=-A/{\rho }_{\mathrm{ch}}^{\alpha }$, where $A$ is a positive constant and $0<\alpha \le 1$. In this paper, exact solutions of spherically symmetric traversable wormholes supported by the GCG are found, possibly arising from a density fluctuation in the GCG cosmological background. To be a solution of a wormhole, the GCG equation of state imposes the following generic restriction $A<(8\pi r_0^2{)}^{-(1+\alpha )}$, where $r_0$ is the wormhole throat radius, consequently violating the null energy condition. The spatial distribution of the exotic GCG is restricted to the throat neighborhood, and the physical properties and characteristics of these Chaplygin wormholes are further analyzed. Four specific solutions are explored in some detail, namely, that of a constant redshift function, a specific choice for the form function, a constant energy density, and finally, isotropic pressure Chaplygin wormhole geometries.

Figure 1

To be a solution of a wormhole, the condition $b(r)<r$ is imposed, so that only the interval below the solid line $r/r_0$ provide wormhole solutions. The plot depicts the values of $\beta =1/3$ and $\beta =1/4$, and one verifies that the wormhole dimensions increase for decreasing values of $\beta$. See the text for details.

Figure 2

To be a solution of a wormhole, the condition $b(r)<r$ is imposed, so that only the interval below the solid line $r/r_0$ provide wormhole solutions. The plot depicts the values of $\beta =1/3$ and $\beta =1/4$, and one verifies that the wormhole dimensions increase for decreasing values of $\beta$. See the text for details.