$N$-body simulation in General Relativity

How would one perform an $N$-body simulation in General Relativity (GR) for something like galaxy formation or galactic dynamics?

Suppose one wants to simulate the rotation curve $v(r)$ for galaxies with an $N$-body simulation, and wants to do it in the framework of GR / the Einstein equations.

Answer

Light++ It is not open source but you can try to contact the author, Werner Benger.

A few years ago we have access to the source code of 'light++'. Not anymore :(

Light++ Raytracer! (general relativistic raytracing)

Simulation of a Black Hole by Raytracing

The Black Earth

About the simulation of galactic close encounters, or a n-body general simulation, under the constraints of GR I found nothing.

EDIT ADD

"I found nothing" can be read like this "there is not a single software package" because, AFAIK,
no one knows how to apply GR in the computation of planetary and galaxy dynamics (small scale with matter).
The Zeldovich approximation is used in the linearization of GR (with caveats):

and has been successfully applied to describe the large scale clustering in the distribution of galaxy clusters. ..However, within the Zeldovich prescription, after a pancake forms in correspondence of crossing of particle orbits, such particles continue travelling along straight lines, ..

I think that your aim is hopeless because GR is around since 1917 and no one succeeded.
Interesting questions, imo:
How close to the reality are the simulations that are performed with Newtonian codes.
What kind of problems we may expect if we are gonna try to do a simulation code.

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