MTW section 25, from eq. 25.16 onwards, derives an orbital equation (with G=c=1, u = M/r, E and L Schwarzschild constants for energy and angular momentum respectively):(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\left(\frac{du}{d\phi}\right)^2 = \frac{M^2}{L^2}(E^2-1) + \frac{2M^2}{L^2}u - u^2 + 2u^3 [/tex]

This equation is readily differentiable to give

[tex]\frac{d^2u}{d\phi^2}= \frac{M^2}{L^2} - u + 3u^2 [/tex]

which is often used for numerical integration to obtain orbital plots of [itex]r[/itex] against [itex]\phi[/itex].

My question: since both equations seem to be well behaved for any [itex]u < \infty[/itex], can they be used to plot the 'infalling' orbit inside the horizon? Or are either E or L or both not valid there?

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# Orbit eq. holds inside BH?

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