Kevin Brown, in his excellent book "Reflections on Relativity" p. 409, "immediately" integrates 2 geodesic equations:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{d^{2}t}{ds^{2}}=-\frac{2m}{r(r-2m)}\frac{dr}{ds}\frac{dt}{ds}[/itex]

[itex]\frac{d^{2}\phi}{ds^{2}}=-\frac{2}{r}\frac{dr}{ds}\frac{d\phi}{ds}[/itex]

to get:

[itex]\frac{dt}{ds}=\frac{kr}{(r-2m)}[/itex]

[itex]\frac{d\phi}{ds}=\frac{h}{r^{2}}[/itex]

Does anyone understand that? I certainly don't.

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# Integral of geodesic equations

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