In a picture or video of a numerical relativity simulation, such as a neutron star merger into a black hole, how do they set up their coordinate system? Lets take the point in a video corresponding to x=10km, y=20km, z=30km, t=1ms. Spacetime itself is distorted, in a very complex way, so how do you make sense of these numbers?
Website to find some nice videos: http://numrel.aei.mpg.de/images
Just to clarify: There are simulations in which space-time is fixed to the a well defined metric (e.g. Kerr black hole accretion disk MHD simulation with no disk self-gravity). But for true numerical relativity, in which the shape of space-time itself has to be simulated, there is no "clean" metric.
Answer
There is a huge variance in how these coordinates are set up, and very often the coordinate systems are chosen for computational convenience (having more data points in place where the metric varies a lot, and fewer far from, say, your colliding black holes), in addition to more physical choices. Once you have run the simulation and have found a solution, however, you can apply math and create any coordinate system you wish for visualizations.
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