Apr. 7th, 2007

synchcola: (heyoka "ok")
oh yeah, i could also talk about what the path of light looks like near a black hole (iirc it gets deflected by
\theta = 2 \bigg(\int_0^{r} {1 \over \sqrt{x^3 - x^2 + (2GM/d)^2}}\,dx\bigg) - \pi
um, "d" is the nearest that the light would get if it stayed on its initial course? and "r" is the denominator's first positive root.)

in maple,

plot(Int(1/sqrt(x^3 - x^2 + C^2), x=0..RootOf(x^3 - x^2 + C^2, x, 0..1))*2 - Pi, C=0..sqrt(4/27), labels=["2*G*M/d", "deflection"], view=[0..0.3846, 0..8]);

yes, the light can go several times around the black hole before escaping! :D

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