spacetimeengine

Yes, the formula is the Einstein's Field Equation. Alas, I don't think it's generally considered as nice and simple. But it's the tool for that: you would basically set an energy density distribution and the software would calculate the metric of spacetime (and that would include time distortion) I guess you can find repos on Github (first Google result for me was this: https://github.com/spacetimeengineer/spacetimeengine) and try your hand. But the theoretical aspect is intimidating, for sure. As for getting up to speed in the theory, I cannot but recommend Leonard Susskind lectures on GR that are available on YouTube. Susskind may be best known as one of the founding fathers of String Theory but the man is an exceptionally great teacher on this subject.

A decade ago when I was interested in General Relativity I wanted to write a simple program to handle symbolic calculations for Einstein field equations (Starting with metric and calculated affine connections, ricci tensor …etc.). Sympy was an option (better because python was the only language I know well) but I found it hard and actually couldn't make it work. I used mathematica which was new for me but did it in a couple of hours. I expanded it later and used it to calculate a lot of things in a black hole paper I published later. I checked now, and it seems that on this front a lot of development in sympy made it possible that we know how very good libraries built on top of it [1] [2]. There is even now a Jupyter notebook example on schwarzschild metric [3]. [1] https://docs.einsteinpy.org [2]https://github.com/spacetimeengineer/spac