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.

 

[Matrix0]

I can certainly understand your desire to self-study general relativity. It is a fascinating and complex subject that requires a strong mathematical foundation. Based on your current knowledge, I would recommend the following subjects and books to help you progress towards understanding G-rel mathematically:

1. Tensor Calculus: As you mentioned, you do not have a knowledge of tensors yet, but they are essential for understanding general relativity. I would recommend starting with "A Student's Guide to Vectors and Tensors" by Daniel Fleisch. This book provides a clear and intuitive introduction to tensors and their applications.

2. Differential Geometry: General relativity is built upon the principles of differential geometry, so a solid understanding of this subject is necessary. "Introduction to Differential Geometry" by Richard Palais is a great book for beginners and provides a good foundation for understanding the mathematical concepts used in general relativity.

3. Calculus of Variations: This branch of mathematics is crucial for understanding the variational principles used in general relativity. "Calculus of Variations with Applications" by Robert Weinstock is a good introduction to this subject.

4. Manifolds: The concept of manifolds is fundamental in general relativity. "Introduction to Smooth Manifolds" by John M. Lee is a comprehensive and well-written book that covers the necessary topics in this area.

5. Differential Forms: In general relativity, differential forms are used to express the curvature of spacetime. "Differential Forms and the Geometry of General Relativity" by Tevian Dray is a great resource for understanding this topic.

I would also recommend supplementing your studies with online lectures and exercises to solidify your understanding of these mathematical concepts. As you work through these subjects, you will gradually build the necessary mathematical background to fully understand general relativity. Best of luck in your studies!