4 To solve this equation, we rewrite it as Integrating it we get where C is a constant of integration and for the sake of convenience we fix C = 1. Integration once more leads to 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. 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 Notice that g$_{22}$ is already continuous, so we don’t need any matching equation for it. The last two equations yield respectively f ′′ f ′ − m + 1 2 ( 1 r − r m r m +1 − b$_{0}$$^{)}$ − α r = − f $^{′}$. (10) f $^{′}$e f = Cr α + 1 $_{2}$+ m 2 √ r m +1 − b$_{0}$ , (11) f ( r ) = ln$^{}$   2 r 1 $_{2}$(3+ m +2 α ) $^{√}$1 − r 1+ m b$_{0}$ $_{2}$F$_{1}$ ( 3+ m +2 α 2+2 m , 1 $_{2}$, 5+3 m +2 α 2+2 m , r 1+ m b$_{0}$ ) √ r 1+ m − b$_{0}$ (3 + m + 2 α )   $_{}$. (12) ds 2 = − ( − M + r 2 l 2 $^{)}$dt 2 + ( − M + r 2 l 2 ) − 1 dr 2 + r $^{2}$dφ$^{2}$. (13) g int $_{AB}$|$_{S}$ = g ext $_{AB}$|$_{S}$ . (14) g int 00 |$_{S}$ = g ext 00 |$_{S}$ , (15) g int 11 |$_{S}$ = g ext 11 |$_{S}$ . (16) 2 R 1 $_{2}$(3+ m +2 α ) $^{√}$1 − R 1+ m b$_{0}$ $_{2}$F$_{1}$ ( 3+ m +2 α 2+2 m , 1 $_{2}$, 5+3 m +2 α 2+2 m , R 1+ m b$_{0}$ ) √ R 1+ m − b$_{0}$ (3 + m + 2 α ) = − M + R 2 l 2 , (17) 1 − b$_{0}$ R 1+ m = − M + R 2 l 2 . (18)