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Oh yes let's talk about my favourite subject ever!
The coolest thing I know of comes from wondering why bent spacetime makes you move at all. The answer is that you always move through time and the bending of spacetime actually turns a bit of time into space and vice versa.
Unnecessary tangent
For a horrible but intuitive explanation of how this works, time is kinda just a direction and bending sorta rotates things so that time looks like it's one of the space directions. Just like turning to the left makes what was your left look like it's straight ahead.This leads to my favourite saying about black holes, once you enter them you can no more escape falling to the singularity than you can escape tomorrow.
I've never heard that take on it before (the idea of turning time into space), but it sounds fascinating. Do you have any links I could follow up on?
Only a few really dry textbooks I'm afraid, it's a subject that's extremely difficult to explain in lay terms as the mathematics is so complicated.
That said if you're feeling masochistic, Schultz's first course in GR is the most approachable that I know.