scenario, we can conclude from this result that it is not possible to satisfy the conditions \[9082013g\] and (\[9082013i\]) simultaneously. In Sec. \[31012014a\], we show that the conditions (\[9082013h\]) and (\[9082013j\]) cannot be satisfied simultaneously either.

Condition (\[9082013j\])
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The assumption that $v$ is constant allows us to rewrite the inequality (\[9082013j\]) in the form $$\gamma \left| \frac{d\Phi}{dr} \frac{dr}{dw} \right| { \put(2,0){$<$} \put(2,-5){$\sim$}\quad \ }g/c^2, \label{26122013a}$$ where, from now on, we denote the left-hand side of this inequality by $f$.

Substituting Eqs. (\[31012014b\]) and (\[10082013g\]) into Eq. (\[26122013a\]) gives $$f= \gamma\frac{r_0S}{2r^2}W^{S/2-1} { \put(2,0){$<$} \put(2,-5){$\sim$}\quad \ }g/c^2. \label{26122013b}$$ To know the maximum value of $f$ during the trip, we need to calculate the local maximums and compare the respective values of $f$ evaluated at these points with the values $f(r_1)$ and $f(r_2)$. If the above inequality holds for the maximum value of $f$, then it holds for any other value. A simple calculation shows that there is only one maximum for $f$ and it is given by $$r_c=\frac{(2+S)r_0}{4}. \label{26122013c}$$ At first glance we could consider this point to be relevant because it is in the domain of $r$ for $S\geq 2$, remember that $r\in(r_0,\infty)$. However, the traveler does not reach this 