How would I start to numerically compute trajectories of Kerr geodesics with constants of motion like in this wikipedia page. I want to recreate trajectories like in this picture in Matlab.
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1 Answer
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A seminal paper on Kerr Geodesics is Wilkins. The necessary equations are found at 2 and 3.
Note that it is not trivial to implement these equations by plugging into an RK4 integrator because of the square roots in the R and Theta "potential" functions.
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$\begingroup$ why recommed the equations with a ± in front of the radial and poloidial derivatives, there are much better equations for numerical integration, see arxiv.org/pdf/1601.02063.pdf#page=3 $\endgroup$– YukterezCommented Jun 5, 2019 at 19:00
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$\begingroup$ Heh, I wasn't aware of that one, it is a bit more recent, cheers! (reading) $\endgroup$ Commented Jun 6, 2019 at 11:45
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$\begingroup$ @Yukterez I really don't know why I didn't mention my own method in my answer, must have been a bit shy at the time . . or just answering the question? I square the Wilkins equations, then use a symplectic integrator to evolve a "pseudo hamiltonian" in Mino time. github.com/m4r35n357/ODE-Playground Incidentally, there are now explicit solutions for the Wilkins equations in Mino time. arxiv.org/abs/1906.05090 $\endgroup$ Commented Nov 21, 2022 at 11:33
sys = geod.system(verbose=True). $\endgroup$