I've been trying to grok General Relativity for a while now, and I've been having some trouble. Many physics textbooks gloss over the subject with an "it's too advanced for this medium", and many other resources start out with something like "well space is just a non-euclidean manifold with a Ricci tensor defined as follows:", which would be cool if I understood non-Euclidean manifolds or Ricci tensors.
Unfortunately, when I try to crack open Wikipedia articles on non-Euclidean articles on the Ricci tensor I have trouble making sense of all the foreign terms.
Is non-euclidean geometry a good place to start if I want to understand general relativity? What's a good introductory resource for non-Euclidean geometry for someone who's only ever dealt with Euclidean?
(Note: I understand the basic principles of general relativity, i.e. how acceleration and gravity are different perspectives about the same thing and how clocks move slower when higher in a gravity field, but I want to understand the math and how it was derived.)
Best Answer
I wouldn't start with learning the maths. Mathematicians take a very different approach from physicists and I doubt it would help much.
You just need the right textbook. I strongly recommend "A first course in general relativity" by Bernard F. Schutz. This seems to me to strike the right balance between understanding the physics and understanding the maths. Note however that even a "first course" is pretty hard work - to get through the book will require much sweat, and I speak from experience :-)