Chaplygin traversable wormholes

TL;DR

This paper derives exact solutions for traversable wormholes supported by the generalized Chaplygin gas, revealing conditions under which such exotic structures can exist and analyzing their physical properties.

Contribution

It introduces new exact solutions for Chaplygin gas-supported wormholes, exploring their properties and the conditions needed for their existence.

Findings

Wormholes violate null energy condition due to exotic matter.

Spatial distribution of exotic matter is localized near the throat.

Multiple specific wormhole solutions are explicitly constructed.

Abstract

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 $p_{ch}=-A/\rho_{ch}^{\alpha}$, where $A$ is a positive constant and $0<\alpha \leq 1$. 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.