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I'd like to build a simulation (realtime) of space ships near a black hole (neutral, still or rotating possibly). Key features would be:

1) the ships are test particles that do not affect the metric

a) possibly test rigid-bodies with GR consistent rotational DOF.

2) the ships can fire their rockets, changing their momentum, and actuate gyros to apply torque.

3) Eventually I'd like to have a toy universe where c is quite low and code a raytracer rendering system that includes lensing, aberrations and the lot. But this is if I manage with 1 and 2.

I did a lot of molecular dynamics in the past so I am familiar with discretisation of equation of motions and the algorithms, however I could not find any clear source for doing so in GR. I also have quite limited GR knowledge so I'm getting a bit lost in length derivations of very special cases.

Does anyone have more insight? Thanks for your help!

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# A Numerical integration of motion

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