- #1
PLuz
- 60
- 0
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...
"[...] 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: