# How to compute Kerr geodesics?

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. • It's better to use Mathematica where packages are already available for computing things like these. – Avantgarde Jun 2 at 7:14
• @Avantgarde thx for your reply. I don't want to use mathematica at first. I startet to implement the ode in Matlab and solved it with standard ode-solver. I'm curious to know how the constant of motions and intial conditions are set up. – almost Jun 2 at 7:26
• Would Computational Science be a better home for this question? – Qmechanic Jun 2 at 7:44
• MATLAB does not seem to have any built-in support for GR. So possibly the best way is first to obtain the system of equations from another system that does have GR support and export it to MATLAB. For example here is SageManifolds notebook for geodesics in Schwarzschild metric, An ODE system ready to export is after the line sys = geod.system(verbose=True). – A.V.S. Jun 2 at 8:05
• @Qmechanic it is already there: scicomp.stackexchange.com/q/32765/20688 – Anton Menshov Jun 5 at 5:14

## 1 Answer

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.

• 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 – Yukterez Jun 5 at 19:00
• Heh, I wasn't aware of that one, it is a bit more recent, cheers! (reading) – m4r35n357 Jun 6 at 11:45