be satisfied simultaneously.

 The conflict between the inequalities (\[9082013h\]) and (\[9082013j\]) {#31012014a}
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It is clear in Eq. (\[15122013d\]) that the condition (\[9082013h\]) ask for high speed. However, from Eq. (\[08012014d\]), we see that the condition (\[9082013j\]) do exactly the opposite. Thus, the best case occurs when we take the largest value of $v$ allowed by Eq. (\[08012014d\]). Taking the equality in Eq. (\[08012014d\]), we find that $$\begin{aligned}
\sqrt{1-v^2/c^2}=\frac{4c^2}{Mg}\frac{S^4}{(1+S)^4}\left[ (S-1)/(S+1) \right]^{S-2}, \label{27122013a}
\\
\nonumber \\
v=c\sqrt{1-B^2}, \qquad B^2=\frac{16c^4}{M^2g^2}\frac{S^8}{(1+S)^8}\left[ (S-1)/(S+1) \right]^{2S-4}. \label{27122013b}\end{aligned}$$

By using Eqs. (\[27122013a\]) and (\[27122013b\]) into (\[15122013d\]), one arrives at $$\frac{4c10^A}{g\sqrt{1-B^2} }\frac{S^4}{(1+S)^4}\left[ (S-1)/(S+1) \right]^{S-2} { \put(2,0){$<$} \put(2,-5){$\sim$}\quad \ }1\ yr. \label{27122013c}$$ In the most favorable case, i.e., $A=6$, $S\to \infty$, and $B\to 0$ ( $M\to \infty$), the left-hand side of this inequality becomes $$\frac{4c}{g e^2}\times 10^6\approx 5\times 10^5\ yr. \label{27122013d}$$ This result is clearly in contradiction with Eq. (\[27122013c\]). Thus, we conclude that the conditions (\[9082013h\]) and (\[9082013j\]) cannot be satisfied simultaneously.

Condition (\[9082013l\]) {#22032014a}
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After some calculations, we find that the left-hand side of the inequality (\[9082013l\]) for the metric (\[10082013c\]) can be written as $$f_1=\frac{Sr_0}{r^3}W_mW^{S-2}. \label{07032014a}$$ One can show that $f_1$ possesses two critical points, which are given by $$r_{\pm}=\left(\frac{1+S}{2} \pm \frac{\sqrt{3S^2-3}}{6} \right)r_0. \label{22082013g}$$ A 