$|\Phi|\ll 1$ at $r_1$. Nevertheless, this result does not seem to be a real problem because the traveler feels force, not potential. The conditions that are related to forces are given by \[9082013g\], (\[9082013j\]), (\[9082013l\]), and (\[9082013m\]). As we will see later, there are values for which these conditions can be satisfied.

Since $\Phi'\approx M/r^2_2=10^{-2A}/M$, the constraint $|\Phi'(r_2)|{ \put(2,0){$<$} \put(2,-5){$\sim$}\quad \ }g/c^2$ is weaker than $|\Phi'(r_1)|{ \put(2,0){$<$} \put(2,-5){$\sim$}\quad \ }g/c^2$. This means that the possible values for $M$ have to be taken from the latter inequality. The substitution of $r_1$ into Eq. (\[15082013c\]) leads to $$|\Phi'(r_1)|=\frac{4S^4}{M(1+S)^4} \left( \frac{S-1}{S+1}  \right)^{S-2}, \label{15082013d}$$ whose minimum occurs when $S$ goes to infinity. Taking this limit ( $M$ is fixed), we obtain $$\lim_{S\to \infty}|\Phi'(r_1)|=\frac{4}{Me^2}. \label{15082013e}$$ Using this in the inequality \[9082013g\], we find that $M{ \put(2,0){$>$} \put(2,-5){$\sim$}\quad \ }5\times 10^{15}\ m$. This is clearly a very large value for $M$, at least if we think of $M$ as being the mass of some spherically symmetric distribution of matter. It is worth mentioning that the above limit is equivalent to taking $\mu \to -2M^2$, that is, we must have $\mu{ \put(2,0){$<$} \put(2,-5){$\sim$}\quad \ }-5\times 10^{31}\ m$.

### Conditions (\[9082013h\]) e (\[9082013i\]) {#6012014a}

Let us assume that 