Possible to self-teach General Relativity?

I have been interested in GR for 6+ years now and when I got into my 2nd year of University I'd had enough of waiting for the 4th year course so I decided to teach it to myself. I bought Relativity Demystified and sat down with it and worked through it. Its got all the mathematics in it and all the physics. The biggest hurdle is the mathematics and notation; the notation adopted by GR (and all similar physics like QFT) could be described as a "generalised vector".

If I have a vector, I could write it in cartesian coordinates as:

$\mathbf{r} = A \mathbf{i} + B \mathbf{j} + C \mathbf{k}$

or polar coordinates as:

$\mathbb{r} = D \mathbb{\hat{r}} + E \mathbb{\hat{\theta}} + \mathbb{\hat{z}}$


But here we are specifying the coordinate system. So I can choose a notation that is coordinate independent, a sort of standardised notation:

$\displaystyle \mathbb{r} = a_1 \mathbb{e_1} + a_2 \mathbb{e_2} + a_3 \mathbb{e_3} = \sum_{i=1}^{3} a_i \mathbb{e_i}$

I then later decide what my coordinates are and I can make the e's become the i's,j's and k's if it is cartesian coordinates we are dealing with.

I have been interested in GR for 6+ years now and when I got into my 2nd year of University I'd had enough of waiting for the 4th year course so I decided to teach it to myself. I bought Relativity Demystified and sat down with it and worked through it. Its got all the mathematics in it and all the physics. The biggest hurdle is the mathematics and notation; the notation adopted by GR (and all similar physics like QFT) could be described as a "generalised vector".

If I have a vector, I could write it in cartesian coordinates as:

$\mathbf{r} = A \mathbf{i} + B \mathbf{j} + C \mathbf{k}$

or polar coordinates as:

$\mathbf{r} = D \mathbf{\hat{r}} + E \mathbf{\hat{\theta}} + \mathbf{\hat{z}}$


But here we are specifying the coordinate system. So I can choose a notation that is coordinate independent, a sort of standardised notation:

$\displaystyle \mathbf{r} = a_1 \mathbf{e_1} + a_2 \mathbf{e_2} + a_3 \mathbf{e_3} = \sum_{i=1}^{3} a_i \mathbf{e_i}$

I then later decide what my coordinates are and I can make the e's become the i's,j's and k's if it is cartesian coordinates we are dealing with.

\mathbf{} (boldface), not \mathbb{} (blackboard bold), which seems to give some odd Hebrew characters when you try to make small letters bold.

Ah, okay. Thanks!

Yeh, the notation gets me confused whenever i've started these books that are too advanced.

Thanks for the recommendation of the book - it sounds excellent. Who is the author "David McMahon and Paul M. Alsing" or "R Wolfson"?

From what i could see the first bits of mathematics i need to learn are 'multivariable calculus' and 'linear algebra'. Would this book even cover these basic techniques in enough detail for me to learn them?

Thanks for responding.

I don't think that an A Level student can understand general relativity in any meaningful sense, and certainly not in a summer. If you really wanted to be able to do all the maths, you'd have to learn:

Multivariable calculus
Linear algebra
Ordinary and partial differential equations
Differential geometry

Plus all of the prerequisites... and the prerequisites for the prerequisites.

General relativity is taught as a third year undergraduate course in Cambridge, and even then I don't think you do anything other than scrape the surface until the fourth year course.

You'd do much better reading popular science books (Brief History of Time, Elegant Universe, QED) in my opinion.

Obviously these are basic problems in MVC, there here so you start to see why its so called.
Linear algebra is basically what was in my first post, learning to deal with vectors and matrices in a more general way. It can be quite a difficult subject to learn but once you get the hang of it, it does tend to make sense.

I'd learn linear algebra and multivariable/vector calculus at the same time, since they're so closely inter-related. When you have a decent enough grasp of calculus, you can start to use the techniques to solve differential equations.

If you are really dead set on trying to learn this stuff you'd do well to pick up a copy of "Mathematical Methods for Physics and Engineering" by Riley, Hobson and Bence. It starts at A Level or below, and works its way up to second/third year material.

Edit: You could try going here and then keep clicking on "Next"...

I recommend reading "Schaum's Outline of Vector Analysis" beforehand, to cover mathematical prerequisites. And Hartle's book Gravity: And introduction to Einstein's General Relativity. It presents a good, intuitive picture for beginners, as opposed to something like De Felice/Clarke.

Okay, i'll have a look into those too. "Mathematical Methods for Physics and Engineering" seems fairly comprehensive, but i'll bare those in mind. "Schaum's Outline of Vector Analysis" is certainly cheap enough, i would have to have a quick look at the other before i buy.

And thanks for making your first post in my thread

Possible to self teach anything though you might be pressed for time in just a summer. I think the biggest caveat here is that to teach yourself things that are mathematical in nature you really need to put in the effort to do practice questions. It's not enough to merely read chapter after chapter in a text book and nod your head as you go along, you have to do the questions at the back of each chapter and that's the really time consuming part and also the part that is hardest to self-motivate for. If you do go ahead with it make sure you use text books that include lots of practice questions, solved examples AND answers (if not full solutions) to questions. (Anything in the Schaum's series is particularly good in this regard but you won't get much than the bare bones with them).

Also never ever buy text books. Always borrow. Though "Relativity Demystified" is relatively cheap I think.

Okay thanks for your help guys.

I'm going to get Mathematical Methods for Physics and Engineering and Relativity Demystified. I'll start on the maths you've stated. Then after a while see how far this gets me into Relativity Demystified.

I'm assuming these maths topics will come up in first year anyway so at the very least it might give me some preperation of what to expect and kill some time.