Spacetime geometry around a black hole

[_Copy/pasted from [YouTube](https://www.youtube.com/user/shiffman/discussion)..._]

Hi Dan,

I love watching your channel and I'd like to offer a coding challenge!

If you search Google Images for "[spacetime geometry around a black hole](https://www.google.co.uk/search?q=spacetime+geometry+around+a+black+hole&hl=en&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjSzMfst43SAhWGLcAKHb6rBgEQ_AUICSgC)" you'll see a multitude of artists impressions of a 'rubber sheet' grid distorted by a central mass, with comparisons between something Earth-sized, a star and finally a black hole. The exact geometry varies widely from one picture to the next.

I think what they're trying to show is the 'excess radius' predicted by relativity. However, I think the Earth only has a theoretical excess radius of a few millimeters, so the rubber sheet would be almost flat, and even the Sun only produces a nominal distortion. Obviously you have to scale these things to see anything, but by how much?

I'd like to see a 3D model made using p5, with sliders to adjust the scale, the mass and the radius of the sphere. The radius is important as a solid body will produce a different geometry to a point-like mass, and when you're considering very large masses there's an interesting point where the surface of the sphere becomes smaller than the Schwarzchild radius.

I did a little digging around to get you started and found what I think would be a useful set of equations at: https://www.physicsforums.com/threads/what-is-feynmans-excess-radius-for-a-black-hole.322567/

What do you think? :-)