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I've been reading the excellent article from Morris and Thorne: "Wormholes in spacetime and their use for interstellar travel a tool for teaching general relativity" and there's something I don't quite get it. In the ninth page the authors state:

"[...] in the general case, the radial coordinate [itex]r[/itex] is ill behaved near the throat; but the proper radial distance [tex]l(r)=\pm \int_{b_0}^{r}\frac{dr'}{(1-b(r')/r')^{\frac{1}{2}}}[/tex] must be well behaved everywhere;i.e., we must require that [itex]l(r)[/itex] is finite throughout spacetime, which also implies that [tex]1-\frac{b(r)}{r}\geqslant 0[/tex] throughout spacetime."

After this very long transcript. My actual question is: why the greater or equal in the last expression? If the quantity is zero the proper radial distance isn't finite...

"[...] in the general case, the radial coordinate [itex]r[/itex] is ill behaved near the throat; but the proper radial distance [tex]l(r)=\pm \int_{b_0}^{r}\frac{dr'}{(1-b(r')/r')^{\frac{1}{2}}}[/tex] must be well behaved everywhere;i.e., we must require that [itex]l(r)[/itex] is finite throughout spacetime, which also implies that [tex]1-\frac{b(r)}{r}\geqslant 0[/tex] throughout spacetime."

After this very long transcript. My actual question is: why the greater or equal in the last expression? If the quantity is zero the proper radial distance isn't finite...

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