Mathematics Required for Introductory G-Rel

[cpsinkule]

I would like to begin some self study of general relativity. I know the math invlolved is quite rigorous so I would greatly appreciate suggestions on books that will put my math level on par with G-rel. I currently have a knowledge of multi-v calc and vector cal (not tensors), linear algebra, and ordinary diff eqs. At this point, I am not quite sure how to progress into the mathematics. So basically, I am asking what subjects\books I need to read in chronological order to eventually have a full understanding of G-Rel mathematically. Again, I am completely lost as to what to do next, so please be specific ;).

 

[BruceW]

I haven't actually learned general relativity, but from what I've heard of it, you'll need to learn the maths about:
Tensors, non-euclidean geometry, curvature of reimannian manifolds.
I'm sure there is a lot more to learn as well. Maybe try this page, and follow the links: http://en.wikipedia.org/wiki/Introduction_to_mathematics_of_general_relativity
And I'm guessing you're already familiar with special relativity? I think that special relativity should be learned before general, since it gives a good introduction to some of the concepts. (And it is correct for inertial frames, when no gravitational field is present).

Edit: sorry I haven't given a chronological order of mathematics you need to learn, or recommended books. But I haven't learned it myself. In fact, I'd also be interested to know what I would need to learn to be able to understand general relativity.

 

[n1person]

Try taking a look at Sean Carrolls Notes on General Relativity (http://preposterousuniverse.com/grnotes/). They do a pretty good job of explaining the necessary math.

 

[pervect]

You can start with an undergraduate GR book, right now, such as "Exploring black holes". I think there were a few others recommended at that level as well.

Personally, I'd recommend learning tensors in the context of electromagnetism first, assuming you have a reasonable background in E&M. Then you'll be somewhat familiar with them when you move onto a graduate level GR book.