1. Sep 27, 2013

### PLuz

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

Last edited: Sep 27, 2013
2. Sep 27, 2013

### Bill_K

No, it would mean the derivative of the proper radial distance dl(r)/dr is infinite. There are plenty examples of functions that remain finite even though their derivative is infinite.