You might get some introductory GR books from the library and browse through them. Examples in rough order of sophistication areMaybe this isnt the right forum for this ... in which case i am sorry
What kind of background would be necssary to even dream about learning General relativity??
Where would be a good starting point?? Maybe at least learn the mathematics involved such as Tensor Calculus (??)
i was told that riemannian geometry is too restricted for general relativity, that it needs to be generalized to pseudo-riemannian geometry to accomodate gr by removing the positive-definiteness of the riemannian metric. and much of riemannian geometry is lost in the transition to pseudo-riemannian geometry, right? like the hopf-rinow theorem no longer holds.of course if you accept that GR is encoded in a riemannian manifold, then it is obvious you want to learn that geometric theory.
Correct, if you replace "much of Riemannian geometry" by "many of the most useful theorems in Riemannian geometry which assume a compact manifold". More generally, many of the crucial distinctions between Lorentzian and Riemannian manifolds involve nice behavior lost because the isotropy group (acting on suitable bundles, e.g. providing "gauge freedom" in the frame bundle I keep yakking about) is no longer compact, which is closely related to the fact that the inner product on tangent spaces is no longer positive definite; see http://www.arxiv.org/abs/gr-qc/9512007 (if this wasn't clear, I am referring to passing from [itex]SO(n)[/itex] to [itex]SO(1,n)[/itex].)i was told that riemannian geometry is too restricted for general relativity, that it needs to be generalized to pseudo-riemannian geometry to accomodate gr by removing the positive-definiteness of the riemannian metric. and much of riemannian geometry is lost in the transition to pseudo-riemannian geometry, right? like the hopf-rinow theorem no longer holds.
I don't agree at all, in fact I think that would be the worst imaginable starting point for someone who has some mathematical aptitude and wishes to quickly learn enough gtr to appreciate the central ideas.i recommend one of einsteins expository essays for the general public.
I'd just add a bit of clarification to a few points:simple explanations... physics is not math... the main point is to try to understand gravitation...I think we give th wrong impression very often that physics can be understood just by learning the mathematical language in which its concepts are expressed...i also recommend taylor wheeler's spacetime physics from 1963, a period when good books on math and science by outstanding figures were being produced for students.
Among other things of interest to physicists!Tensors are just notation for writing down and quantifying curvature.
I am going to go out on a limb here and guess that you are attending lectures at your local university on theoretical physics for physics students. If so, since these students often cannot be assumed to be familiar with the neccessary mathematical concepts/techniques, it is reasonable for lecturers to spend time explaining the technical background. It is indeed unfortunate that this need inevitably tends to discourage extensive discussion of physical issues! Still, if my guess is correct, the problem might be that you are placing unreasonable expectations upon the lecturers--- if you could find a group of physics students who like you already know the math, perhaps you could engage in discussion of the good stuff!As a mathematician I have been very disappointed in many lectures supposedly on physics which contained no physics, just math i already knew.