- #1
Orion1
- 973
- 3
The solution for the Schwarzschild metric is stated from reference 1 as:
[tex]ds^2=- \left(1-\frac{r_s}{r}\right) c^2 dt^2 + \left(1-\frac{r_s}{r}\right)^{-1}dr^2+r^2(d \theta^2 +\sin^2 \theta d \phi^2)[/tex]
The solution for the Schwarzschild metric is stated from references 2 as:
[tex]ds^2 = \left(1 - \frac{r_s}{r} \right) c^2 dt^2 - \left(1 - \frac{r_s}{r} \right)^{-1} dr^2 - r^2 \left(d \theta^2 + \sin^2 \theta d \phi^2 \right)[/tex]
The solution for the Schwarzschild metric is stated from references 3 as:
[tex]ds^2 = \left(1 - \frac{r_s}{r} \right) c^2 dt^2 - \left(1 - \frac{r_s}{r} \right)^{-1} dr^2 - r^2 \left(d \theta^2 - \sin^2 \theta d \phi^2 \right)[/tex][tex]r_s[/tex] - Schwarzschild radius
There is a difference in the sign of the elements between the stated solutions.
Which is the correct solution?
Reference:
http://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution
http://en.wikipedia.org/wiki/Tolman-Oppenheimer-Volkoff_equation#_ref-ov_3
http://en.wikipedia.org/wiki/Schwarzschild_metric
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