# Good books on both Relativities

1. May 20, 2013

### JamesOrland

Hello. I'd like to hear opinions on good books about either/both Relativities. I have some knowledge of the workings of Special Relativity, and naught but the barest knowledge of General Relativity beyond the basic verbal descriptions, so I'd like to know about good books on that.

2. May 20, 2013

### tensor33

One of my personal favorites is General Relativity by Hobson,Efstathiou, and Lasenby. It has a chapter in the beginning that gives a good review of special relativity. You can find it as a free PDF online.

3. May 20, 2013

### Staff: Mentor

How much math do you know?

4. May 20, 2013

### JamesOrland

A lot of Calculus and Linear Algebra, very little differential geometry.

5. May 20, 2013

### Bandersnatch

6. May 20, 2013

### WannabeNewton

I recommend "A First Course in General Relativity" - Bernard Schutz. It is an introductory book covering both special and general relativity.

7. May 22, 2013

### HomogenousCow

I had alot of issues with that book, there were too few examples for me to grasp the concepts comfortably. Also not a big fan of the comma and semi colon notation.

8. May 22, 2013

### WannabeNewton

Hey there friend :)! I'm not a fan of the comma and semi colon notation either, in fact I despise it. It isn't aesthetically appealing and I find it quite annoying to write down and keep track of. As far as examples go, yes there is quite a lack of examples in Schutz but it isn't as bad as Wald haha - there are literally no examples in Wald. Hartle, if I recall, has tons of examples and Carroll has a good number of examples as well. I agree that examples are very important in being able to allow a reader to get closer to solving problems.

9. May 22, 2013

### bcrowell

Staff Emeritus
For SR, the best intro for someone at your math level is Taylor and Wheeler, Spacetime Physics.

For GR, a couple of relatively easy books to start with are:

Taylor and Wheeler, "Exploring Black Holes: Introduction to General Relativity"

Hartle, "Gravity: An Introduction to Einstein's General Relativity"

10. May 23, 2013

### zn5252

Personally, I had to learn tensor calculus beforehand. Then Started with Schutz book, then Callaghan book on Space-time geometry, then the master of them all : Gravitation by MTW - but do not only read , you have to do every exercise in MTW. Do not spend one hour or two per Ex, if you can not do it, but rather spend days if not weeks ! this way you will learn - Consult all references therein, they are invaluable . See also online Ex from Caltech.
See also in parallel, other books for each theme, e.g. Weinberg, Dirac, Landau(outstanding book), Parmanbhan's, Eric Poisson's, Wald and others...
Watch also the online video lectures by Kip Thorne, by Susskind.
Do not only read the books, but rather taste the beauty !

11. Jun 2, 2013

### JamesOrland

For SR, then, Spacetime Physics by Taylor and Wheeler is a good one, I gather?

And for GR, I should learn tensor calculus (something I've been putting off for lack of time), and these books will cover the rest, do you think?
From what you've said, good books are Schutz, Taylor and Wheeler, Hartle and MTW - by the way, who's MTW? - is that right?
If there's more input to be heard, I'd love it. Still, thank you for your replies so far! ^^

12. Jun 2, 2013

### PAllen

Especially the second of these is really of historic interest only. It is very old notation, very incomplete set of topics even for introductory work by modern standards. If you want to bother with it for 'touching history' I would go for the paperback modern edition which has several appendices added by Einstein up through 1953 (including on cosmology). The link above is just the original 1921 lectures, when not much was yet understood about GR.

Don't get me wrong - I have the second one, I enjoy reading it to touch history and see how Einstein was thinking about things, but it is a ridiculous choice to learn GR from.

13. Jun 2, 2013

### PAllen

A lot depends on your goals. If you want to reach reasonable real understanding quickly, but are not planning this as an area of research or advanced study, I think studying tensor calculus first is not efficient. I would endorse the Hartle and Carroll suggestions as the place to start (Hartle first). Then see if you want more. You will have learned quite a bit if you simply do Taylor and Wheeler, then Hartle, then Carroll.

(MTW is "Gravitation" by Misner, Thorne, and Wheeler. It is a over 1100 pages long, is great to own but I would not recommend it as an efficient way to get started. Note also, it has not been updated since 1973 or so.)

14. Jun 2, 2013

### WannabeNewton

I should tell you that the kind of tensor calculus you learn from a proper manifolds text will not be the kind of tensor calculus used in introductory GR texts. The math texts will present tensor calculus in a very abstract, coordinate free way and few intro GR texts do calculations using such a formalism. Instead, in an intro GR text, you will be shown some theory and then you will get acquainted with the index based approach for calculations (which can be extremely powerful if used correctly). As such, it is better to just learn it from a GR text.

Actually, a recent GR text by Straumann actually does many calculations using a coordinate free approach. Mathematically it is a quite advanced and, as such, is quite an awesome book.

PAllen has already given great suggestions but I would just like to add that if you are planning to go with GR for a while, then throw in Wald's text in there as well. Actually if you do all the exercises in Wald and completely work out his in-text calculations, you will have mastered the kind of tensor calculus / tensor algebra that shows up in various classical GR papers / textbooks.

15. Jun 2, 2013

### Bill_K

I'm compelled to mention the online lecture notes by Winitzski, which strive to be coordinate free.

16. Jun 2, 2013

### WannabeNewton

Wow, very nice Bill thank you for this Now I have a free resource I can point my math friends to (*looks at micromass*) when they complain that the index based calculations in Wald make their eyes bleed lol

17. Jun 3, 2013

### Markus Hanke

This is excellent, thank you for this link !

18. Jun 3, 2013

### Markus Hanke

Same here. Personally, in my own notes, I always use the "bar" notation :

$$A_{|i}$$

for the partial derivative, and

$$A_{||i}$$

for the covariant derivative. In fact this is how I first learned it, and I think it is much clearer than the comma and semicolon notations.

19. Jun 3, 2013

### WannabeNewton

I see. I have never seen that notation before myself but if it works for you then all the power to it :)! Wald exclusively uses $\nabla_a$ for the derivative operator on space-time and $\partial_{a}$ as well as $\frac{\partial}{\partial x^{a}}$ for partial derivatives so this is the notation I have become accustomed to, as well as prefer.

20. Jun 3, 2013

### George Jones

Staff Emeritus
I can't resist ...

My copy of Zee's new book "Einstein Gravity in a Nutshell" arrived a few days ago.
I personally find that coordinate-free notation can sometimes be useful for calculation, and that coordinate-free notation often is useful conceptually. When reading about hypersurfaces a while ago, I found that (in increasing order of abstractness) Poisson's "A Relativist's Toolkit", Gourgoulhon's "3+1 Formalism in General Relativity", and Lee's "Reimannian Manifolds" were all useful.

General relativity is, however, a physical theory. Anyone that wants to use GR as a physical theory has to be able to do calculations that use "index gymnastics".

I have an older version of Straumann, which I really like. But I don't shy away from books that use an index-only approach.

Last edited: Jun 3, 2013