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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]
[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]
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