I want to do a short practice to see how mass evolve space and how space curvature evolve mass distribution.

Most of the GR simulations were rather complicated but I think the black hole binary had become quite standard especially with LIGO's success, and I did saw some PPTs from the early 2000s about the topic.

Is there one or two popular papers about the math and pseudo code on the black hole binary simulation? i.e. for beginners?

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    $\begingroup$ Only the far field gravitational wave equations are relatively simple, but if you want to look at the strong field of a black hole merger you still need a supercomputer, see here $\endgroup$
    – Yukterez
    Feb 12 at 20:09
  • $\begingroup$ @Yukterez the accuracy was not the concern, it can be two $200^3$ block(0.016 GB tensor) or $200^4$ block (3GB tensor). I want to write a simulation on the simplest case of the strong field as a practice to learn. I looked the video and found "The Einstein Toolkit", but that's too powerful an example than what I'm looking for. $\endgroup$ Feb 23 at 6:38

1 Answer 1


There is no "easy way" to do numerical relativity. People had been working on numerical solutions to GR since the beginnings of computers, and there were bits of success over the decades. It took until a major breakthrough in 2005 for the first binary black hole simulations. These were seen as the holy grail of numerical relativity, since you had to handle moving singularities to make it work.

The breakthrough builds on decades of technical research answering questions about to how to handle time stepping, how to determine self consistent initial conditions, and what to do with singularities (infinities).

Three research groups independently figured things out:

The three papers are short. But they are challenging to read unless you are familiar with some technical GR (the ADM formalism in particular) and numerical methods for solving PDEs (like adaptive mesh refinement).

  • $\begingroup$ Thank you!! This is very useful. I learned that the black hole binary had some advantages in the error handling of the the initial value and may greatly reduce the complexity of the simulation, and thought it might worth a try. $\endgroup$ Mar 4 at 6:28

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