Reference book for mathematics in relativity

[Axe]

Please suggest a good book which deals with the whole mathematical description of relativity (special theory as well as general theory, with tensor analysis). Also it would be much appreciated if the description was not very concise, as i am not an expert in the subject. Much Appreciated. :)

 

[haushofer]

Nakahara's "Geometry and topology in Physics" is imo a very nice compromise between physical application and mathematical rigor.

 

[Axe]

Nakahara's "Geometry and topology in Physics" is imo a very nice compromise between physical application and mathematical rigor.

Thank you. I will have a look. But what exactly does this book cover? Does it cover the entire aspect of general relativity?

 

[Chestermiller]

I've found that the book Vector Analysis With and Introduction to Tensor Analysis by A. P. Wills (a Dover Publication) presents the material very effectively, and covers all the material needed to study GR. I'm not sure whether it is still in print, but you may be able to get a copy from Amazon.

Chet

 

[Axe]

I've found that the book Vector Analysis With and Introduction to Tensor Analysis by A. P. Wills (a Dover Publication) presents the material very effectively, and covers all the material needed to study GR. I'm not sure whether it is still in print, but you may be able to get a copy from Amazon.

Chet

Thanks Chet. But as the name suggests, is it just a book on tensors? or it analyzes GR in advance, like defining the structure of space according to GR.

 

[Chestermiller]

Thanks Chet. But as the name suggests, is it just a book on tensors? or it analyzes GR in advance, like defining the structure of space according to GR.

It is something in-between. It explicitly anticipates that the reader will probably be studying GR, and includes sections on multidimensional manifolds, curved manifolds, parallel transport of vectors, covariant differentiation, Riemann tensor, Ricci-Einstein tensor, curvature scalar. One thing I like about the development is that it consistently carries the coordinate base vectors and base one form vectors (aka reciprocal basis vectors) throughout. As an engineer, this works well for me.

I've been writing up some notes on vector and tensor analysis, specifically customized to SR. If you are interested in receiving a copy, let me know via a private message. I will glad to email it to you.

chet

 

[Axe]

It is something in-between. It explicitly anticipates that the reader will probably be studying GR, and includes sections on multidimensional manifolds, curved manifolds, parallel transport of vectors, covariant differentiation, Riemann tensor, Ricci-Einstein tensor, curvature scalar. One thing I like about the development is that it consistently carries the coordinate base vectors and base one form vectors (aka reciprocal basis vectors) throughout. As an engineer, this works well for me.

I've been writing up some notes on vector and tensor analysis, specifically customized to SR. If you are interested in receiving a copy, let me know via a private message. I will glad to email it to you.

chet

Thanks a ton for the help Chet. :)
I will be very happy to study your notes. Please send me a PM (Private Message).

 

[JM]

I am also looking for a good book on SR, with emphasis on the physics. I have Einsteins 1905 paper and I am comfortable with it except for the 'twin paradox' in section 4. I also have French, Taylor and Wheeler, and Born, and I have read many others. They don't deal very well with questions such as whether the moving clocks use the same units as the stationary ones or whether they 'tick' at a different rate. Or with 'world lines',and related concepts.
Can you suggest a good beginner book?
JM

 

[Munnkeyman]

I'd recommend an Introduction to Tensor calculus, Relativity and Cosmology by D.F. Lawden.

Sorry can't include links, yet.
amazon.com/Introduction-Calculus-Relativity-Cosmology-Physics/dp/0486425401

It's slightly old-school though, but a very well laid out book and concise.

 

[Mark M]

In addition to the textboooks recommended, here is a lecture series by Sean Carroll.

 

[julian]

Ray D'Inverno covers a lot of the maths and does calculations in detail and you don't have to learn the somewhat abstract index-free formulation or exterior calculus etc. first.