a star or a planet, then it is impossible to have a traversable wormhole. Nevertheless, we can still consider the possibility of having a different kind of matter that may meet the requirement \[9082013n\]. The so-called dark matter, for example, would clearly satisfy this condition, since it does not couple strongly with ordinary matter.

The matter distribution
-----------------------

To have an idea of how the matter that generates the wormhole of the Wyman solution is distributed over space, let us see how the density of mass-energy behaves in the frame of the static observers. Using the metric (\[10082013c\]) in $\rho$ as given by (\[9082013p\]), one finds that $$\rho=-\frac{S^2-1}{32\pi Gc^{-2}}\frac{r_0^2}{r^4}W^{S-2}, \label{5012014c}$$ which is negative for $S>1$. This means that the static observers see negative mass-energy density. Therefore, Wyman’s solution does not satisfies the requirement \[9082013r\]. Note that, for $S>2$, the mass-energy density goes to zero as $r$ goes to $r_0$. This is in agreement with the result of Sec. \[04022014b\].

Final remarks {#1032014d}
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We have shown that the Wyman solution contains wormholes for $S>1$ without using the cut-paste technique[^4]. For $S>2$, the two regions of the wormholes become flat as we walk away from the throat. In this case and 