Learning General Relativity: What Do I Need to Know?

[Sankaku]

There are really three tiers at which you can really learn anything substantive about general relativity.

This is a good general description.

"General Relativity From A to B" by Robert Geroch

This is a great book for tier 1. Here is an amazon link:
https://www.amazon.com/dp/0226288641/?tag=pfamazon01-20

It is possible to understand a huge amount of general relativity without any math beyond algebra.

Dr. Crowell knows what he is talking about. He has a free Relativity e-book here:
http://www.lightandmatter.com/genrel/
Although it lies on tier 2 of Nabeshin's post.

There is one more book that is somewhat unusual. Once you have some calculus under your belt, try this:
https://www.amazon.com/dp/1589880447/?tag=pfamazon01-20

In general, don't let the discussion of all the requirements put you off. One of the great things about GR is how it draws together many of the most interesting parts of Math and Physics. Hopefully, you can see that as good motivation to learn all these other topics!

 

[Cbray]

I don't think I've ever face palm'd myself as hard before I read this post.
You're obviously thinking GR is something you can do after learning basic mechanics off reading for a couple of weeks or months, at your level it would take you about a few years to learn multi-variable calculus, linear algebra (and other mathematical tools), and learn probably at the least a first year undergraduates physics course to just dip your toes in GR if you work about 4 hours a day.

OR you can just read a basic book on it to give you a description of it, or Brian Greene documentaries that make me livid.
By all means, just learn single-variable calculus then learn basic Newtonian mechanics up to conservation of angular momentum, and then read about special relativity.

 

[Matterwave]

I don't think I've ever face palm'd myself as hard before I read this post.
You're obviously thinking GR is something you can do after learning basic mechanics off reading for a couple of weeks or months, at your level it would take you about a few years to learn multi-variable calculus, linear algebra (and other mathematical tools), and learn probably at the least a first year undergraduates physics course to just dip your toes in GR.

OR you can just read a basic book on it to give you a description of it, or Brian Greene documentaries that make me livid.
By all means, just learn single-variable calculus then learn basic Newtonian mechanics up to conservation of angular momentum, and then read about special relativity.

Why would you facepalm over an interested student? Are we not supposed to be encouraging of the younger generation rather than trying to be elitist? I see no benefit to the argument "oh, you're too young, this is too complicated, forget about it".

For the low-level GR, I always recommend Lilian R Lieber's "Einstein's Relativity" https://www.amazon.com/dp/1406765236/?tag=pfamazon01-20.

You do need to know some algebra to understand that book, but that'd be about it.

It's pretty outdated since it was written in the 50's I believe, and so its concepts of "vector" and "tensor" are explained from a "transformational properties" perspective. But, for the quickest and easiest introduction, I think this book is best.

 

[Cbray]

Why would you facepalm over an interested student? Are we not supposed to be encouraging of the younger generation rather than trying to be elitist? I see no benefit to the argument "oh, you're too young, this is too complicated, forget about it".

For the low-level GR, I always recommend Lilian R Lieber's "Einstein's Relativity" https://www.amazon.com/dp/1406765236/?tag=pfamazon01-20.

You do need to know some algebra to understand that book, but that'd be about it.

It's pretty outdated since it was written in the 50's I believe, and so its concepts of "vector" and "tensor" are explained from a "transformational properties" perspective. But, for the quickest and easiest introduction, I think this book is best.

I'm happy for her to be interested, we no doubt need more people interested in physics. I'm still only a two years older than her and she is probably as keen to learn, I just face palm'd since it sounded funny and it was me thinking how naive the question was.

 

[dkotschessaa]

I'm happy for her to be interested, we no doubt need more people interested in physics. I'm still only a two years older than her and she is probably as keen to learn, I just face palm'd since it sounded funny and it was me thinking how naive the question was.

It was unnecessarily elitist, since the amount of math you described is not even necessary to get through Einstein's own Relativity: The Special and General Theory.

"The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler. I make no pretence of having withheld from the reader difficulties which are inherent to the subject. On the other hand, I have purposely treated the empirical physical foundations of the theory in a "step-motherly" fashion, so that readers unfamiliar with physics may not feel like the wanderer who was unable to see the forest for the trees. May the book bring some one a few happy hours of suggestive thought!"

- Albert Einstein - from the introduction