Some books to bridge the gap before GR

[cr7einstein]

Hi all,
I am extremely interested in GR, but somehow feel that the books I read are not really enough. Frankly, I find many question on this site and elsewhere completely bewildering, which makes me think that I don't have a solid foundation, especially in classical mechanics and various mathematical techniques. Here's a list of books I have read:

MATHEMATICS(After pre calculus and basic calculus)

Mathematical methods for physicists(Still working my way through) By Arfken and Weber

Advanced calculus by David Widder

Ordinary differential equations by Coddington

Principles of mathematical analysis by Rudin

Vector Calculus

Tensor calculus by Barry Spain

RELATIVITY

Introduction to special relativity by Resnick

Gravity by Hartle

General relativity with applications to astrophysics by Straumann (newly acquired)

I have a few books on dynamics, nuclear physics, etc, but they are quite unnecessary. I am not much into QM, and have only read Griffith's. I also have, as a reference, PRINCIPLES OF PHYSICS by Resnick and Walker.

All my knowledge of classical mechanics and lagrangian formulism is from pdf versions of Feynman's lectures. Please suggest me some books that will fill the gap I have left out. Just to be clear, I want to read Mathematical theory of black holes by Chandrahekhar next, so I want to know where I need to improve before proceeding.

NOTE: I am still in high school, and I don't have any professor to help me out, so the books should be suitable for self study. All the same, they should be properly rigorous.
EDIT: I am not very comfortable with the exercises suggested in most of the books (esp. Mathematical methods for physicists and both the GR books. Though I have no conceptual glitches, I really want to be able to solve the exercise problems, as doing so is both satisfactory and rewarding. Any suggestions on that( how to be more efficient)? Am I going too far too soon, and maybe need to stop down and consult a book which will perhaps give me a good foundation to solve the exercises, or a book with excellent exercises? If so, which one?
2 : Of course, I have viewed the lectures by Susskind.

Thanks!

 

[WannabeNewton]

I think you're trying to jump way too far ahead prematurely. If you can't solve the exercises then you do have conceptual glitches. People often say they understand the concepts but can't solve the problems which doesn't make much sense. How much EM do you know? If you don't know EM at the level of Griffiths then you should work on that first. Also, did you try to learn (intermediate) classical mechanics from a proper book like Taylor (i.e. not the Feynman lectures)? If not then that's also something you should work on.

The Susskind lectures are pretty useless for anyone who wants to have a truly serious understand of GR so unless you're watching them for entertainment (which is totally cool) you aren't going to get anything out of them. Stick to the foundations before jumping into GR, it will only help you. If you try to get into GR before getting EM and classical mechanics down cold then you're going to struggle immensely to the point of stagnation.

 

[cr7einstein]

@WannabeNewton , I was thinking the same as well. I have done EM from Griffiths, but only partially. I thought (wrongly) that it was unnecessary for GR, and my knowledge of EM is limited to that required for SR. I have only done Classical mechanics from online sources (such as feynman's lectures and various pdf lecture notes). I was planning to buy a good book on classical mechanics, but I am confused between Goldstein and Taylor. Which is the better one? I want it to be properly rigorous and not leave out any topic just for pedagogical reasons. Any suggestions on that?
Also, can you suggest any other book to bet a better build up for GR? Is Spain's enough, or do I need more Tensor calculus? What about SR?
Thanks

 

[WannabeNewton]

I have done EM from Griffiths, but only partially. I thought (wrongly) that it was unnecessary for GR, and my knowledge of EM is limited to that required for SR.

You'll need to have a very solid grasp of (at the very least) the content of Griffiths in order to effectively learn most of advanced physics including GR.

I have only done Classical mechanics from online sources (such as feynman's lectures and various pdf lecture notes).

That's definitely not going to be enough.

I was planning to buy a good book on classical mechanics, but I am confused between Goldstein and Taylor. Which is the better one? I want it to be properly rigorous and not leave out any topic just for pedagogical reasons. Any suggestions on that?

Goldstein would be the ideal choice assuming you're comfortable with the foundations of mechanics at the level of e.g. Kleppner and Kolenkow. Otherwise I would go with Taylor first because Goldstein would be too steep a jump otherwise. Rigorous isn't necessarily good; most of the times it isn't. You need to know the physics first before meandering into superfluous rigor.

Also, can you suggest any other book to bet a better build up for GR? Is Spain's enough, or do I need more Tensor calculus? What about SR?
Thanks

I have no idea what Spain (not the country!) is personally. Just focus on mechanics and EM for now. Often I find that people (including myself) get really excited at the start to learn a subject and collect all the necessary resources for it but quickly become demotivated by the overwhelming sea of material before them. Don't worry about GR and just try to make the most of Griffiths etc. because if you try to learn these subjects with the sole intent of getting to GR then you won't learn them thoroughly.

 

[atyy]

Tensor calculus by Barry Spain

This uses "old style" definitions of a tensor, which are that a tensor is an object that transforms in a certain way. That's fine, but it also helps if one uses the more modern definition of a tensor, which is a tensor is a multilinear map of vectors to a numbers.

You can find the relationship between the old and new approaches in eg.
https://www.amazon.com/dp/0521231906/?tag=pfamazon01-20
https://www.amazon.com/dp/0521845076/?tag=pfamazon01-20

Because GR is uses linear algebra in the tangent space of a manifold, it is helpful to have elementary linear algebra too.
https://www.amazon.com/dp/0071794565/?tag=pfamazon01-20
https://www.amazon.com/dp/1258812584/?tag=pfamazon01-20