I get a message at least once a week asking me to explain something about black holes.
Maybe half the time I can answer the question in a way that's satisfactory to the asker. But the other times, it ends up boiling down to the fact that more than any other physics theory, it goes hand-in-hand with the math. GR is difficult.
Please learn Differential Geometry. I get a lot of horseshit responses like "if you can't explain it to a five-year-old, you don't understand it" This is unrealistic horseshit. It would sure be nice if everything were simple enough that this facile bullshit were true. But there are many things for which it is not. Also it depends on the level of understanding you want to have and the "explain it to a five-year-old" level of understanding is generally not what the geriatric 40-year-olds that make up most of NG's population are looking for when they reach out to me.
You need to be comfortable with four-vectors, there are lovely clifford algebra texts you can get great mileage out of without needing to know anything beyond the elementary levels of ordinary differential equations and undergrad linear algebra. Tensor analysis is important to apply the Differential Geometry to curved spacetime.
Read John Lee's intro to smooth manifolds
And then the follow-up texts on topological and riemann manifolds
And also (in parallel or before) bishop's tensor analysis book is great.
And if these texts (which are introductory and fully intended for undergrad consumption) are too difficult, then the prereqs are too much and you should settle for a more smooth-brained grasp of GR, which you can get from laymen texts by guys like michio or brian green, etc.
Going forward, I'll be referring most questions to this post.
Ka-ne
WOW, you sound passionate about what you do.
Maybe I'll read those books, they sound interesting.