Wormhole proper radial distance

  • Thread starter PLuz
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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...
 
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Bill_K
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My actual question is: why the greater and equal in the last expression? If the quantity is zero the proper radial distance isn't finite...
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.
 

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