Books and Plan to Study Relativity (SR and GR) in Detail

[Sunnyocean]

Hi,

I am a Physics graduate and I am VERY mathematically inclined. (This does NOT mean I know a lot of math. My curriculum focused on experimental physics - which left me with a very keen desire to study all the mathematics involved - so I do need to start from scratch.)

I would like to study and understand the Special and General Theory of Relativity in as much detail as possible. I do have some background in SR (I got acquainted with it A BIT), but I would like to understand not just "a lot more" but EVERYTHING there is to understand about both SR and GR. In other words, I would like to (re-?) start studying it from scratch, until I understand it perfectly (as "perfectly" as it is humanly possible).

I have read similar discussions on this forum and the more I read, the more confused I became.

I would be very grateful if someone could give me a detailed list of books that I can read in order to not only understand SR and GR, but also MASTER the mathematics involved (yes, the epsilon and delta of it).

Please note that I am not looking to "get acquainted" or to "use shortcuts". I am looking for the hard sttuff, both the mathematics and the physics. (Yes, those books on manifolds, differential geometry etc.).

I am definitely not looking for "summarized explanations" or for books that state theorems without proofs (whether physics books or mathematics books).

If possible, I would also like a plan or "timeline" (e.g. "first study this book, then this other book etc.") that takes into consideration both the physics and the mathematics involved, and the respective books (good books / authors please).

I just don't know which are the best books and in which order I should start.

I know calculus (but not multivariate calculus), high school geometry including space geometry (but not non-Euclidean geometry), and I have some knowledge of vectors. I do "know" vector calculus but I only know how to apply a few theorems / concepts (del, div, Laplace) in a 3D Euclidean space, but not how to derive thosse theorems / concepts. (I am trying to give you an idea of my mathematical background).

Please help and thank you very much in advance for your time and help.

 

[fresh_42]

One of the most recommended sources I've seen here on PF is
https://arxiv.org/pdf/gr-qc/9712019.pdf

 

[Sunnyocean]

Hi fresh 42,

Thank you for your reply but lecture notes that claim to teach General Relativity in 238 pages is exactly what I am *not* looking for.
I need a detailed learning plan, including books that explain the mathematical concepts in great detail.
I had a look at the lecture notes and I am afraid I find them lacking.

 

[kent davidge]

Start with math books that are used in universities around the world. If you are a graduated student, so you have some idea to get started.

 

[vanhees71]

For SR an GR I usually recommend Landau&Lifshitz vol. II. Another very good book is Stephani, Relativity. More advanced is Weinberg, Gravitation and Cosmology. If you like it very modern (Cartan form calculus) the standard book is Misner, Thorne, Wheeler, Gravitation (aka "the phone book"). Then there's also the lecture notes by Blau:

http://www.blau.itp.unibe.ch/Lecturenotes.html

 

[smodak]

1. Hartle's Gravity https://www.amazon.com/dp/0805386629/?tag=pfamazon01-20

2. Moore's workbook https://www.amazon.com/dp/1891389823/?tag=pfamazon01-20

BTW, Sean Carrol also has a book based on the lecture note but I would not use that as my first introduction - it has 513 pages :) This is a very good book.

And stay away from Schutz :)

 

[Dr Transport]

Dated, but Adler, Bazin and Schiffer isn't bad to start out with, it starts with vectors and tensors and works its way forward. Resnik's book on SR is a decent intro and gets the point across.

all the modern texts tent to move ahead quickly, but like I mentioned above the older texts tended to be methodical and more complete.