content_image/345228.jpg content_image/345229.jpg
Similarly, the EoS parameter ω becomes 

<img src='content_image/345228.jpg'>

We would also comment that the case of vanishing pressure p = 0 (dust) is not allowed in the present formalism since it will make f ( r ) unbounded. The dust cases in the framework of braneworld wormholes are investigated in [22, 23]. 

The specific dimensionless parameter ξ , defined by ξ = ( p − ρ ) / | ρ | , characterizes how the exotic or normal matters are distributed around the wormhole’s throat [4, 15]. The exoticity at or near the throat of the wormhole is required to be non-negative, ξ > 0. The positivity of the exoticity ensures that wormhole will satisfy the flare-out condition as well. From Eq. (15), the exoticity becomes 

<img src='content_image/345229.jpg'>

In Fig. 5, we have plotted the exoticity against the radial coordinate. It shows that the exoticity remains positive while it converges to zero for large r . Hence the wormhole is surrounded by the exotic phantom energy, right from its throat to a sufficiently large distance. This also suggests that we can construct a wormhole with a sufficiently large radius that could be traversable for two dimensional beings. 

In summary, our objective in this article has been to present a mathematical prescription for obtaining a wormhole in low dimensional spacetime. The wormhole is supported by an external source of phantom energy which is anistropically distributed. The wormhole spacetime satisfies a variable equation of state, which is in good agreement with earlier models available in the literature. It is also shown that the otherwise asymptotically non- flat wormhole could be converted to an asymptotically flat one by matching the various components of its metric with the exterior BTZ spacetime. 

[1] M. Visser, Lorentzian Wormholes: From Einstein to Hawking, (Springer-Verlag New York, Inc, 1996) 

[2] M. Jamil et al, arXiv:0906.2142v1 [gr-qc] 

