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Coordinate integral

  1. Dec 9, 2008 #1
    I'm looking at Gullstrand-plainleve coordinates in Kerr metric. While on the whole, it seems pretty straight forward, I found the integral aspect a little inaccessible. I've had a look at various web pages regarding integrals but to be honest, I don't know where to start with the following. Any insight would be appreciated.

    [tex]\delta=a^2sin(2\theta)\int_r^{+\infty} \frac{v\Omega}{\varpi^2}dr[/tex]

    where

    [tex]\Omega=\frac{2Mar}{\rho^2(r^2+a^2)+2Ma^2rsin^2\theta}[/tex]

    [tex]\varpi^2=r^2+a^2+\frac{2Mra^2}{\rho^2}sin^2\theta[/tex]

    [tex]v=\frac{\sqrt{2Mr(r^2+a^2)}}{\rho^2}[/tex]

    [tex]\rho^2=r^2+a^2cos^2\theta[/tex]
     
    Last edited: Dec 9, 2008
  2. jcsd
  3. Dec 10, 2008 #2
    I used an online integral calculator (replacing r with x) which produced the following results-

    [​IMG]

    Does this look right? (unfortunately it didn't have the means to incorporate the limits of r and +∞. What impact would that have on the results?).

    online integral calculator-
    http://integrals.wolfram.com/index.jsp
     
    Last edited: Dec 10, 2008
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