Introduction to GR. ¿Gron or Collier?

[smodak]

I've looked a bit closer at Gron's book. I think it's very nice, and of course it assums that you are familiar with calculus, but it develops all the needed vector calculus (using the Ricci calculus) on pseudo-Riemannian manifolds needed for GR. It gives a lot of details in the derivations of the formulae. So I think it's great for a beginner to learn the subject, which is not that easy to get used to.

I completely agree.

 

[atyy]

And as a "amateur" physicist?

Yes, I'm an amateur, which means the only aspect I'm an expert on is quantum interpretations :P

 

[atyy]

BTW, Gron's book assumes you know calculus. I'm pretty sure one could not read it unless one has had calculus. It'd be more accurate to say that it develops differential geometry.

I think it is hard to learn differential geometry from Gron's book alone. I recommend

Crampin and Pirani
Applicable Differential Geometry
https://books.google.com.sg/books/a...ial_Geometry.html?id=iDfk7bjI5qAC&redir_esc=y

Marián Fecko
Differential Geometry and Lie Groups for Physicists
https://books.google.com.sg/books?id=vQR0mN1dgUEC&redir_esc=y

 

[smodak]

I've looked a bit closer at Gron's book. I think it's very nice, and of course it assums that you are familiar with calculus, but it develops all the needed vector calculus (using the Ricci calculus) on pseudo-Riemannian manifolds needed for GR.

BTW, Gron's book assumes you know calculus. I'm pretty sure one could not read it unless one has had calculus. It'd be more accurate to say that it develops differential geometry.

This is true. Gron's book assumes the knowledge of calculus while Collier's book does not.

 

[ibkev]

From my cursory flip though of Collier's book, someone who tried to read it and had no prior knowledge of calculus wouldn't get very far. It does give a taste of the math involved and seems to offer a nice overview of the topics that you need to learn in more depth to be a serious student of the topic.

That said the rate at which it takes a reader through the topics is such that I don't think anyone would describe it as "rigorous".

• The first 155 pages takes the reader from their first exposure to algebra (there's literally a table that shows y=2x for different values of x, which is a head scratcher) to overviews of calculus, linear algebra, vector calculus, Newtonian mechanics and special relativity including Minkowski metrics and 4-momentums by page 155.
• The next 100 pages or so takes the reader from an intro to manifolds through to the Schwartzchild metric, Ricci tensor, geodesics in schwartzchild spacetime and showing how GR is tested by things like perihelion advance.
• The last 50 pages are about black holes and cosmology.

The book is very much a survey - to me it's value is that it gives the reader a sense for the various mathematical moving parts involved in GR, the connections between them, and how they all hang together. In all, not a bad road map/primer for in GR.

 

[almarpa]

Thank you all for your replies.

I think I will use Gron (perhaps supplemented with Collier, for a different view and more examples).
Most of you agree that Gron is a nice introduction to the subject, and opinions from such distinguished forum contributors is really important for me.

Hope to count with your help when I get lost with Gron's explanations (which I am pretty sure it will happen when I get to contravariant and covariant vectors)

Once I master it, maybe I will try with Zee.

 

[vanhees71]

To avoid the confusion right away: There are no contravariant and covariant vectors but only contra and covariant components of vectors with respect to a basis, at least in a Riemannian or pseudo-Riemannian manifold.

 

[almarpa]

I am already having problems with these concepts, you see...

 

[NathanaelNolk]

It seems to me you have the level suited for studying GR out of Schutz's book. May I ask what books you learned physics with? You said you were self-studying. Can you solve problems, or do you have only a theoretical understanding?
If you thoroughly studied the physics subjects that you listed I see no reason not to go straight to Schutz.

 

[almarpa]

I am telecommunications engineer, now working as a teacher.
In adition to my formal education as an engineer, and focusing in pure physics, I have studied classical mechanics from Kleppner - Kolenkow and Morin's books, and electrodynamics from Griffiths' book. I have also read something from Griffiths' QM book, but I still can not claim to have studied it. Sure I can solve problems, that is what I mean when I say that I have studied a book. That is why it takes me so long to complete a book.

 

[NathanaelNolk]

Did you work through the problems too? If so, I think you are ready to tackle Schutz. His special relativity chapter will be valuable if the only SR you have seen comes from K&K or the likes. What's more, if you find it too difficult, you can always go back to easier books.

 

[almarpa]

Ok, I will take a look Schutz book as well. I think I saw it at the library.

Tanks for the advice.

 

[almarpa]

I have checked reviews in amazon for Schutz's book, and self learrners do not seem to be very pleased with it.

I think I will keep on going with Gron.

Thanks.

 

[smodak]

I have checked reviews in amazon for Schutz's book, and self learrners do not seem to be very pleased with it.

I think I will keep on going with Gron.

Thanks.

Yup I had purchased Schutz (especially because of the solution manual) but hated it. I had used Gron, Collier, Foster-Nightingale (the third edition is a really great book), and Susskind GR lectures to get a good overview of the subject before delving into other books.

 

[ibkev]

I'd be curious if you ever tried Hartle? I saw that Sean Carroll recommended it once as a precursor to his book.

Also, what was it about Schutz that didn't speak to you?

 

[smodak]

I'd be curious if you ever tried Hartle? I saw that Sean Carroll recommended it once as a precursor to his book.

Also, what was it about Schutz that didn't speak to you?

I like Hartle. I can read and understand Schutz now (that I know GR) but it was very confusing for me and boring to read when I started. What had really helped me was simultaneously (when I felt like) using Gron, Collier, Foster-Nightingale, and Susskind lectures together along with this short video. I did have most of the Math Pre-Requisites when I started.

If you have most of the prerequisites, another fantastic book to learn GR from is
https://www.amazon.com/dp/1891389823/?tag=pfamazon01-20

Some solutions for the book are available http://www.physicspages.com/index-physics-relativity/thomas-a-moore-a-general-relativity-workbook/

 

[almarpa]

I have heard good things about Hartle, but it is not available at my library. I can not buy a book that I have not reviewed before.

 

[almarpa]

Yesterday I checked Moore's book on general relativity and I found it really interesting.

Would you say that it is at the same level than Gron, or maybe (as it seemed to me) it is one or two steps more difficult?

If so, would it be a good starting point instead of Gron's?

Regards.

 

[smodak]

Yesterday I checked Moore's book on general relativity and I found it really interesting.

Would you say that it is at the same level than Gron, or maybe (as it seemed to me) it is one or two steps more difficult?

If so, would it be a good starting point instead of Gron's?

Regards.

Hard to compare. I like having multiple books available to be consulted. Moore's book is actually a workbook - he starts with very rudimentary explanation of and then takes you through steps. I believe it could be used as a second book after Gron to make sure concepts are solidified (as long as you can actually go through all the steps and finish the book).

 

[almarpa]

Just curious, what was your roadmap to learn general relativity?

 

[smodak]

Just curious, what was your roadmap to learn general relativity?

Nothing in particular. I read some books here. Some books there. Watched some videos until I got the general idea. Then I just read different stuff from different books. That's how I always read. Take a bunch of books and read different stuff from them. I cannot follow a roadmap especially since this is for fun.

 

[vanhees71]

Yesterday I stumbled over another great book on GR:

Peter Hoyng, Relativistic Astrophysics and Cosmology, Springer (2006)

The title is a bit misleading, because it is really a very nice introduction into GR, treating the math (differential geometry of pseudo-Riemannian manifolds) boiling it down to the essentials but very well motivated and thoroughly derived. E.g., it gives the best introduction to the Fermi-Walker transport of tetrades and the associated physics like the Thomas precession in SR and the geodetic precession I've ever seen. Without sacrificing understandability and derivations of the mathematical foundations it comes quickly to the physics (Einstein's field equations), the Schwarzschild solution, Oppenheimer-Volkoff (stars), black holes, gravitational waves, and finally FLRW. It's a great introduction enabling one to read more detailed books like Weinberg's on the subject.

 

[smodak]

Yesterday I stumbled over another great book on GR:

Peter Hoyng, Relativistic Astrophysics and Cosmology, Springer (2006)

The title is a bit misleading, because it is really a very nice introduction into GR, treating the math (differential geometry of pseudo-Riemannian manifolds) boiling it down to the essentials but very well motivated and thoroughly derived. E.g., it gives the best introduction to the Fermi-Walker transport of tetrades and the associated physics like the Thomas precession in SR and the geodetic precession I've ever seen. Without sacrificing understandability and derivations of the mathematical foundations it comes quickly to the physics (Einstein's field equations), the Schwarzschild solution, Oppenheimer-Volkoff (stars), black holes, gravitational waves, and finally FLRW. It's a great introduction enabling one to read more detailed books like Weinberg's on the subject.

The book looks really good. UGH! Now I will have to get this book :(

 

[smodak]

Not to confuse the OP more but here is a very good synopsis of some books.

http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html

 

[almarpa]

No confusion. I have finally decided to go with Gron.

 

[George Jones]

Not to confuse the OP more but here is a very good synopsis of some books.

http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html

This list is good, but it is very out-of-date. Examples too recent to be on the list include GR books (in roughly ascending order of level) by

Collier
Gron and Naess
Moore
Hartle
Zee
Hobson, Efstathiou, and Lasenby (who bought me a beer in Banff)
Ryder
Plebanski and Krasinski
Straumann
Gron and Hervik
Carroll
Padmanabhan

some of which have been mentioned in this thread.

 

[almarpa]

Great contribution, George!

This is just what I needed to make up my mind.

I am surprised to see Zee up in the list. I thought it was at the same level than Carroll.