need for maximal extension).

Conditions \[9082013b\], \[9082013cc\], \[9082013c\] and \[9082013d\] {#19022014a}
---------------------------------------------------------------------

From Eq. (\[10082013h\]) and the fact that $r\in (r_0,\infty)$, we have $1-b/R\geq 0$ everywhere.

The condition $w \to \infty \Rightarrow b/R \to 0$ is clearly satisfied, since $b/R \to 0$ as $r\to \infty$. However, when $w\to -\infty$, which is equivalent to $r\to r_0$, we have $b/R \to -\infty$ for $S>1$ \[see Eq. (\[10082013h\])\]. Hence, the condition \[9082013cc\] is not satisfied.

It is evident from Eq. (\[10082013g\]) that $\Phi$ is finite for $r>r_0$.

From Eq. (\[10082013g\]), we see that the condition \[9082013d\] is not satisfied because $w\to -\infty$ (the same as $r\to r_0$) implies $\Phi\to -\infty$.

It is clear that the object that we are studying is not a Morris-Thorne wormhole. Nevertheless, we are going to prove now that it is indeed a wormhole. The candidate to be the throat is the two-surface $t=constant$, $R=constant$. Applying these constraints to Eq. (\[10082013a\]), one gets $$ds^2_2=-R^2(d\theta^2+\sin^2\theta d\phi^2) \label{27062014a}$$ and $$\partial_{n_{\pm}}=\pm \sqrt{1-b/R}\ \partial_R, \label{27062014b}$$ where $\partial_{n_{\pm}}$ is the unit normal vector with plus sign for $r>r_m$ and the minus one for $r_0<r<r_m$. Finally, using Eqs. (\[27062014a\]) and (\[27062014b\]) into Eq. (\[26062014b\]), we arrive at $$tr(K)=\mp 2\frac{\sqrt{1-b/R}}{R}, \label{24062014h}$$ where $tr(K)$ stands for $g^{ab}K_{ab}$. 