A First Course in General Relativity by Schutz

[micromass]

• Author: Bernard Schutz
• Title: A First Course in General Relativity
• Amazon Link: https://www.amazon.com/dp/0521887054/?tag=pfamazon01-20
• Prerequisities:

 

[WannabeNewton]

One of the best intros to the subject if you are ok with non rigorous mathematics. The chapter on gravitational waves is jut plain awesome from a physics standpoint.

 

[Fredrik]

This book is a great place to learn special relativity, maybe the best. It also has a very nice introduction to tensors. So I strongly recommend the book for those parts of it. If you want to learn SR and the most basic stuff about tensors³, in my opinion, this is the book to buy.

When I got to the part about GR, I didn't like its treatment of differential geometry, so I started learning differential geometry from Spivak¹ and general relativity mainly from Wald².

This book has a reputation for being the easiest (or at least one of the easiest) introductions to GR, and it probably is. But the reason it's easy is that it does everything it can to avoid differential geometry.


*) Spivak is very good, but I think Lee is better.
**) Wald is very good, but people seem to like Carroll better. (I haven't even looked inside it, so I don't know).
***) It explains dual spaces, dual bases, and multilinear maps $T:V_1\times\cdots\times V_n\to\mathbb R$, where each $V_i$ is either V or its dual V*, and V is an arbitrary finite-dimensional vector space. This is the most basic stuff about tensors. In differential geometry (and therefore in GR), V is a tangent space of a smooth manifold, but if I recall correctly, Schutz doesn't really explain those concepts. So the book has an excellent treatment of tensors outside of the context of differential geometry, but a (deliberately) very weak presentation of differential geometry.

 

[WannabeNewton]

This book has a reputation for being the easiest (or at least one of the easiest) introductions to GR, and it probably is. But the reason it's easy is that it does everything it can to avoid differential geometry...

So the book has an excellent treatment of tensors outside of the context of differential geometry, but a (deliberately) very weak presentation of differential geometry.

This seems to be true of many *undergraduate* GR texts. They all seem to take this "physics first" standpoint which may work for some undergraduate students but me personally I cannot stand all the hand waving. If you are just coming out of your first intermediate mechanics class then this book or Hartle will probably do you justice but if you have already learned smooth manifolds (I have looked at spivak's volume 1 and the problems are brutal compared to the ones in Lee haha) then this kind of book would probably move too slowly in terms of the mathematics. In that case Wald is probably a *considerably* better choice (or Carroll but like you I think Wald is better because he is more precise with the math). The thing is though, books like Wald tend to focus on the math SO much that the down to Earth physics gets totally lost and for things like that a book like this would be pretty good (like I said the chapters on gravitational waves and the one on interior solutions for stars). Anyways if the person wanting to start GR feels he/she is not ready to do a graduate level text but finds the math in the typical US undergraduate texts like Hartle move too slow I still hold strong that the book by Hughston and Tod works well to bridge the gap but it assumes prior knowledge of SR (this book is used for undergraduate applied math majors at Oxford). By the way Fredrik have you checked out the book on SR by Rindler. IMO that book is the best out there for SR; it covers things like Thomas Precession which Schutz doesn't.

 

[Fredrik]

By the way Fredrik have you checked out the book on SR by Rindler. IMO that book is the best out there for SR; it covers things like Thomas Precession which Schutz doesn't.

I have not. I mean, I know I've had a quick look inside it at some point, but I don't even remember what I thought at the time.

I don't mind if a book leaves out specific things that can be useful or interesting. I would say that there are two main types of books, introductory texts and reference texts. Books like Spivak and MTW belong to the latter category; they try to cover everything. What I require from an introductory text isn't complete coverage. I just want it to explain the most basic things really well.

 

[elfmotat]

This was my first GR textbook. It certainly got the job done, and I've yet to find anything else I'd recommend to a beginner. It certainly wasn't my last GR textbook though. You'll definitely want a more advanced text once you've given this one a read-through.

 

[QGravity]

This book alongside "Gravity - An Introduction To Einstein General Relativity" by James Hartell & "Relativity, Gravitation & Cosmology - A Basic Introduction" by Ta-Pei Cheng make strong foundation for more advanced treatments such as "Gravitation - Foundation & Frontiers" by T.Padmanabhan & "General Relativity" by R.Wald