Math for GR: Branches & Building Blocks

[shounakbhatta]

Hello,

Can somebody tell me what are the different branches of mathematics required as building block of GR?

 

[andrien]

http://en.wikipedia.org/wiki/Mathematics_of_general_relativity

 

[shounakbhatta]

Yes, that part I know, but anything more specific.

 

[ShayanJ]

The main thing you should know is Riemannian geometry and then tensor calculus

 

[haushofer]

I always recommend Nakahara's topology and geometry book. That pretty much covers everything you need to know for GR and is accessible if you know linear algebra and the usual calculus stuff.

 

[bcrowell]

You can learn GR at many different mathematical levels. The following books use little or no math:

Geroch, "General Relativity from A to B"
Gardner, "Relativity Simply Explained"
Einstein, "Relativity: The Special and General Theory ," http://etext.virginia.edu/toc/modeng/public/EinRela.html

These books use nothing beyond freshman calculus:

Taylor and Wheeler, "Exploring Black Holes: Introduction to General Relativity"
Hartle, "Gravity: An Introduction to Einstein's General Relativity"

So to answer your question, we'd really need to know something about your goals. At what level do you want to understand GR? If your goal is to dive into a graduate text, then we could discuss that.

Also, what is your background in physics? This is much more likely to lead to problems than a lack of mathematical background.

 

[shounakbhatta]

Hello Ben,

The books you have mentioned are wonderful. I would like to go for Hartley. However, can you please advise me whether I should go for the following book on Linear Algebra by Gilbert Strang. Please remember, I am a self learner, so too much advanced or less illustrative boo would be difficult for me. Please find below the link:

http://www.cambridgeindia.org/showbookdetails.asp?ISBN=9788175968110

-- Shounak

 

[bcrowell]

I think it might be helpful to know a small amount of basic linear algebra before you try Hartle.

 

[shounakbhatta]

Yes, that is why I was asking about the book; the link which I have sent.

-- Shounak

 

[George Jones]

Taylor and Wheeler, "Exploring Black Holes: Introduction to General Relativity"

The second edition of Taylor and Wheeler (and now Bertschinger) should (finally) be out in month or two. The second edition has a much better treatment of cosmology, but I am curious if the second edition will have features that I dislike.

I think it might be helpful to know a small amount of basic linear algebra before you try Hartle.

And some Calc III, i.e., Hartle uses partial derivatives and a few multiple integrals.