- #1
stephen cripps
- 15
- 0
Homework Statement
The step I am trying to follow is detailed here where I am trying to get from equation 6.26:
[tex]t=\int_{r_1}^{r}(1+\frac{2M}{r}+\frac{b^2V(r)}{2}+\frac{Mb^2V(r)}{r})dr[/tex]
to equation 6.30
[tex]t=\sqrt{r^2-r_1^2}+2Mln(\frac{r+\sqrt{r^2-r_1^2}}{r_1})+M(\frac{r-r_1}{r+r_1})^{1/2}[/tex]
Homework Equations
[tex]V(r)=r^{-2}(1-\frac{2M}{r})[/tex]
[tex]b=r_z(1-\frac{2M}{r_1})^{-1/2}\approx r_1(1+M/r_1)[/tex]
The Attempt at a Solution
I tried simplifying the equation by subbing in V, however my integral:
[tex]t=\int_{r_1}^{r}(1+\frac{2M}{r}+\frac{b^2}{2})(\frac{1}{r^2}-\frac{2M}{r^4})dr[/tex]
seems to get nowhere near the required answer when integrated.