($2+1$)-dimensional wormhole from a doublet of scalar fields

We present a class of exact solutions in the framework of $(2+1)$-dimensional Einstein gravity coupled minimally to a doublet of scalar fields. Our solution can be interpreted upon the tuning of parameters as an asymptotically flat wormhole as well as a particle model in $2+1$ dimensions.

Figure 1

$B(r)$ versus $r$ [Eq. (27)] for various values of $\eta =5.0,1.0,0.5,0.1$, and 0.0 from top to bottom, respectively, with $\xi =-1,\epsilon =1,r_0=1$.

Figure 2

$B(r)$ versus $r$ [Eq. (27)] for various values of $\eta =5.0,1.0,0.5,0.1$, and 0.0 from top to bottom, respectively, with $\xi =1,\epsilon =-1,r_0=1$.

Figure 3

(a) From top to bottom [Eqs. (35)–(38)]; $K$, $R_{\mu \nu }{R}^{\mu \nu }$, $\rho$, and $R$ versus $r>b_0$ (b) $B(r)$ (dashed) and $\eta f(r)$ (solid) in terms of $r$ for $r>b_0$. For both we set $b_0=1$, $\epsilon =-1$, and $\xi =-1$.

Figure 4

$B(r)$ versus $r$ from Eq. (27) for various values of $\eta =5.0,1.0,0.5,0.1$, and 0.0 from bottom to top, respectively, with $\xi =-1,\epsilon =-1,r_0=1$.