How do I go about learning GR?

[Frogeyedpeas]

Hello guys, so I have a problem. I am familiar with a fair bit of physics but I cannot seem to cross the gap between classical to relativistic physics. If someone could give me a road map on how to get to GR that would be helpful. For those of you wondering this is where I am at.

Mathematics:

Calculus I (Well Understood)
Calculus II (Well Understood)
Calculus III (I have trouble with the vector portion, and am not totally familiar with the whole 3-d lot of things, but I get the idea and am working on it right now)
Ordinary Differential Equations (Pretty Well Understood, I am still working on it but I've got down the idea of characteristic roots, laplace transform, homogenous etc..., separation of variables, exact, repeated differentiation for solutions... still working on figuring out integral equations etc...)
Partial Differential Equations (Absolute Newbie, can only do separation of variables (although I could probably deduct my way through some))
Linear Algebra (Absolute Newbie, I'm quite familiar with matrices and matrix equations, tensor equations etc... but still not a pro and not at all aware of the basics such as eigenvalues)
Multilinear Algebra (Absolute Newbie)
Matrix Calculus (Absolute Newbie, I'm trying to work my way through it and it is becoming awfully difficult)
Tensor Calculus (Can't say I know anything...)
Topology (Absolute Newbie, although I conceptually can visualize and understand a lot if I'm given an explanation for stuff)
Differential Geometry (Absolute Newbie)
Differential Topology (Absolute Newbie)

And I believe if I make it through that list I will have all the background mathematics to pursue GR.

Physics (a lot shorter list):

Newtonian Mechanics (Well Understood)
Special Relativity (Somewhat Understood, I understand all the formulas, how to apply them, and I understand how some of them are derived conceptually but others such as the energy-mass equivalence and lorentz transform are still unknown to me how they are derived.)
General Relativity (I see the formula, I get that its a tensor formula, and I get the general idea that we are relating the topological curvature to the actual spatial metric to the energy density but I cannot deal with it mathematically or work with it at all)

I don't know how much further I need to move, if somebody could give me a road map of what to master in what order to fully grasp GR it would be greatly appreciated.

 

[Matterwave]

To fully grasp GR, you would need a lot more preparation, but you certainly can begin learning GR now. Most GR textbooks at the introductory level will introduce the concepts of differential geometry and tensor calculus that you need for GR.

 

[skippy1729]

It might be worthwhile to look at:

The Foundations of the General Theory of Relativity. A. Einstein contained in:

The Principle of Relativity - A Collection of original papers on the Special and General Theory of Relativity. Dover Publications.

This is an English translation of Einstein's original paper. It was aimed at physicists of the period who were not, on the whole, familiar with tensor calculus or Riemannian geometry. As a result it is largely self-contained and introduces these concepts in an informal manner with physical motivation. It is extremely clear and well written. The other papers in the book are classics and the Dover publication is inexpensive. I found it to be very suitable for self-study. The notation is not modern but modern notation, while elegant, can be confusing to newcomers.

Good Luck.

 

[king vitamin]

You mentioned that you're working on Calc 3 "not totally familiar with the whole 3-d lot of things." If you're talking about vector calculus, I'd recommend that you concentrate on that - I think that knowing vector calculus at an advanced undergraduate level (enough to work through an undergrad EM book) really helps with tensor calculus, which is just a few steps from that. I think Linear Algebra helps too (it's tied in with vecot/tensor calc), and of course understanding special relativity well can only help you.

 

[Frogeyedpeas]

Thanks for your responses... So based on what I heard, If I just grab one of those volumes and read up some more on vector calculus, I will have enough background to start understanding GR?

I btw own a book called Matrix and Tensor Calculus with Applications to... by Aristotle D. Michal which is published by Dover Publications... Is that a good book to use? Because it seemed like a very easily digestable read but as I continued to read into it I noticed that it got very difficult extremely fast and soon it was well beyond what I'm used to.

Should I keep working with it?

Additionally,

for each of the Mathematics topics above what books should I get to better learn them because I still have no background on differential geometry or topology right now, which if I'm not mistaken, is very important for grasping relativity

 

[George Jones]

Calculus III (I have trouble with the vector portion, and am not totally familiar with the whole 3-d lot of things, but I get the idea and am working on it right now)
Linear Algebra (Absolute Newbie, I'm quite familiar with matrices and matrix equations, tensor equations etc... but still not a pro and not at all aware of the basics such as eigenvalues)

Learn the stuff in Calculus III and some introductory linear algebra.

Newtonian Mechanics (Well Understood)

Have you studied Lagrangian mechanics? If not, you should study an introduction to this.

Special Relativity (Somewhat Understood, I understand all the formulas, how to apply them, and I understand how some of them are derived conceptually but others such as the energy-mass equivalence and lorentz transform are still unknown to me how they are derived.)

You probably should read the short, excellent book A Traveler's Guide to Spacetime: An Introduction to the Special Relativity by Thomas A. Moore. After this, start reading Gravity: An Introduction to Einstein's General Relativity by James B. Hartle,

https://www.amazon.com/dp/0805386629/?tag=pfamazon01-20.

Also, read right now the following paper by Hartle, a professional relativist, on his perspective on how general relativity should be taught:

http://arxiv.org/PS_cache/gr-qc/pdf/0506/0506075v2.pdf.

Even though I am interested in some of the more mathematical aspects of general relativity, I strongly agree with Hartle that tensors and differential geometry can wait until after substantial familiarity with general relativity has been built up (section V in the paper). I think this is particularly true for folks learning general relativity by self-study.

 

[lalbatros]

I used two sources to learn GR:

1) Gravitation by Misner, Charles W.; Kip S. Thorne, John Archibald Wheeler
2) The Classical Theory of Fields, by L D Landau and E.M. Lifgarbagez

Their approach is extremely different.
Both books are written by legends of physics.

Ref (1) needs a lot of time to read, but it is terribly motivating and fun to read.
Ref (2) can be read rather quickly, but it is also much more austere and needs more initial background. However, the approach is specially interresting, as it is mainly based on the least action principle.