content_image/371006.jpg content_image/371007.jpg content_image/371008.jpg content_image/371009.jpg content_image/371010.jpg content_image/371011.jpg content_image/371012.jpg content_image/371013.jpg content_image/371014.jpg
To solve this equation, we rewrite it as 

Integrating it we get 

<img src='content_image/371006.jpg'>

<img src='content_image/371007.jpg'>

where C is a constant of integration and for the sake of convenience we fix C = 1. Integration once more leads to 

<img src='content_image/371008.jpg'>

Here $_{2}$F$_{1}$ is a hypergeometric function representing a series expression. It should be noted that logarithmic form for f ( r ) have been obtained for a MT wormhole in (3+1)-dimensions as well [10]. Also notice that f ( r ) does not give a finite value as r → ∞ , so the solution is not asymptotically flat. Hence we may match this interior solution to an exterior vacuum spacetime at a junction radius R [17]. Notice that in (2+1) dimensions, the only exterior vacuum solution is the stationary BTZ spacetime [18, 19], given by 

Here M corresponds to mass of the spherically symmetrical object while l = 1 / √ − Λ > 0 and Λ < 0 is the cosmological constant. In order to match the interior wormhole solution with the exterior BTZ solution, we impose the continuity of the metric coefficients, g$_{AB}$ , across a surface S , i.e. 

<img src='content_image/371009.jpg'>

<img src='content_image/371010.jpg'>

The wormhole metric is continuous from the throat radius r = r$_{0}$ to a finite distance r = R . Explicitly Eq. (14) can be written as 

<img src='content_image/371011.jpg'>

<img src='content_image/371012.jpg'>

Notice that g$_{22}$ is already continuous, so we don’t need any matching equation for it. The last two equations yield respectively 

<img src='content_image/371013.jpg'>

<img src='content_image/371014.jpg'>

