[zifk]

Simulations require supercomputers for doing large scale, detailed calculations, but simple situations can be solved completely analytically. For example, gravitational time dilation can be calculated somewhat simply for a central gravitational potential: https://en.wikipedia.org/wiki/Gravitational_time_dilation#Ou...

General Relativity is incredibly math heavy but fundamentally the numerical methods involved are standard methods for differential equations. The hard part is going from the math to a solvable form. See https://arxiv.org/pdf/2008.12931 for a broad overview. This will of course probably not make sense without an introduction to differential geometry, a beast of a topic itself. See some big textbook like https://arxiv.org/pdf/2412.08026 or find yourself a copy of Gravitation by Misner, Thorne and Wheeler.

[floxy]

>an introduction to differential geometry

I did find "Functional Differential Geometry":

https://mitp-content-server.mit.edu/books/content/sectbyfn/b...

...which uses Scheme to teach differential geometry. I would need to learn quite a bit more before tackling that book. Maybe something like: "Structure and Interpretation of Classical Mechanics"?

https://mitp-content-server.mit.edu/books/content/sectbyfn/b...

...but even there, it looks like I would need to start with something more basic.