Relativity Introduction to GR. ¿Gron or Collier?

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The discussion centers on selecting an introductory book on General Relativity (GR) between Gron and Collier. Gron’s book is noted for its step-by-step approach and detailed calculations, while Collier is seen as more structured but potentially less rigorous. Participants express concerns about the lack of calculus prerequisites in both books, arguing that a solid mathematical foundation is essential for understanding GR. Suggestions for additional resources include other introductory texts and lecture notes, but the focus remains on finding a suitable book for self-learners. Ultimately, Gron's book is favored for beginners looking for a rigorous yet accessible introduction to the subject.
almarpa
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Hello all.

I am self teaching physics, and after completing Classical Mechanics (Special Relativity included), Classical EM and an introductory course to QM, I would like to take a very introductory look to General Relativity.

With this purpose in mind, I have chosen 2 books, and I would like to buy one of them:

1) Gron - Naess "Einsteins Theory for the mathematically untrained".
2) Collier "A most incomprehensible thing".

I have taken a look to both of them, and I have seen that they follow quite different approaches. Collier seems to be more "ordered" (fiist the basis of needed mathemathics, then Newtonian gravitation, Special relativity, Manifolds, curvature, Einstein's equations, etc.) while Gron introduces all this concepts as needed. Besides, Gron does not even metion thing like "manifolds", "one-forms", etc. (I guess he uses them anyway, but with different names, maybe). On the other hand, Gron is a physics teacher specilized in GR, so I guess his book must be more rigorous.

I wonder if anyone could suggest me which of these books is best suited, or has better expplanations.

Thanks in advance.
 
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Well, for the beginner I'd not recommend to learn GR using the full machinery of the Cartan calculus which is quite unintuitive (at least for me, who is trained in the "old fashioned" Ricci calculus). I don't know Gron's book very well and Collier's book not at all. I think Gron's book is very good, because he shows many steps in the calculations often omitted from usual textbooks. My favorite as an introduction to GR (and by the way also E&M) is Landau-Lifshitz vol. II. Another more physics than math oriented book is Weinberg, Gravitation and Cosmology (1971). If you want to address also the modern Cartan calculus (with forms and all that), the good old Misner, Thorne, Wheeler is good too.
 
Thanks for the reply.

The adicional books you suggest seem to be too advanced for me, so, for the time being:
Gron: 1
Collier: 0

Any other opinions?
 
Both are equally good - see the previews in Amazon / Springer website and pick the one you like better.
 
Do either of these books assume you understand calculus of variations or lagrangians?
 
ibkev said:
Do either of these books assume you understand calculus of variations or lagrangians?
No
 
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No. Both them consider you could even not be familiar with calculus.
 
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almarpa said:
No. Both them consider you could even not be familiar with calculus.

Must be a silly book if it does GR without assuming that you're familiar with calculus. Why don't you study up on the math and study GR from an actual good book.
 
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micromass said:
Must be a silly book if it does GR without assuming that you're familiar with calculus. Why don't you study up on the math and study GR from an actual good book.

Sorry to disagree but the books are not silly at all. They actually teach you the basics of calculus and all the required math. Now do they teach you calculus or all the math fully? No. But they teach you enough for you to understand the material.

I do agree, however, that it would be advisable to learn calculus before tackling GR :) You could still study GR from any of the two above books.
 
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  • #10
smodak said:
Sorry to disagree but the books are not silly at all. They actually teach you the basics of calculus and all the required math. Now do they teach you calculus or al the math fully? No. But they teach you enough for you to understand the material.

They don't make you understand the material. They make you think you understand the material. Big difference.
 
  • #11
Keep in mind that any of this books will not be my last general relativity book. This will be just a "apetizer" before reading Schultz's, Zee's or Carroll's book, for example.

Nevertheless, remember that I am self - lerning physics as a hobby. I would not enjoy studying from a book for which I am not still prepared.

Thanks all.
 
  • #12
micromass said:
They don't make you understand the material. They make you think you understand the material. Big difference.
Haha. Nothing can make me do anything :) But seriously, take a peek at the books - you might change your opinion.
 
  • #13
smodak said:
Haha. Nothing can make me do anything :) But seriously, take a peek at the books - you might change your opinion.

What makes you think I didn't look at the books? I already did.
 
  • #14
almarpa said:
Keep in mind that any of this books will not be my last general relativity book. This will be just a "apetizer" before reading Schultz's, Zee's or Carroll's book, for example.

Nevertheless, remember that I am self - lerning physics as a hobby. I would not enjoy studying from a book for which I am not still prepared.

Thanks all.

Of course, but why waste your time on a book that won't teach you the material properly. Just do it properly from the beginning.
 
  • #15
micromass said:
What makes you think I didn't look at the books? I already did.

I stand corrected then. I apologize for the confusion.
For me, they were a great starting point although I already knew the required math.
 
  • #16
Of course!

I am open minded to receive different suggestions for a good introductory book to GR.
Gron's book seemed OK for that objective, but maybe you know different options.
 
  • #17
almarpa said:
Of course!

I am open minded to receive different suggestions for a good introductory book to GR.
Gron's book seemed OK for that objective, but maybe you know different options.

My suggestion is then to study a bit more on the required mathematics. It will make things in GR much much much more clear. If you can intuitively grasp the mathematical idea of a manifold or a differential variety, you will have much less problems with GR.

Sure, if you want to delve right into GR, then the books in the OP are good. But personally I wouldn't be able to understand much of them if I didn't know the mathematics already.
 
  • #18
Yes, that is why I need a book that teaches not only the physics, but the required mathematics as well. I am used to read this kind of books.
For example, Griffiths EM book provides, in the first chapter, the vector calculus required to be able to flollow the rest of the book.
Is there a similar book for GR?

Regards
 
  • #19
almarpa said:
Yes, that is why I need a book that teaches not only the physics, but the required mathematics as well. I am used to read this kind of books.
For example, Griffiths EM book provides, in the first chapter, the vector calculus required to be able to flollow the rest of the book.
Is there a similar book for GR?

Regards

There probably is such a book for GR. But I can't help you further if that's what you want since I think it's a very bad idea to learn the required mathematics from physics books, especially GR books.
 
  • #20
OK.

Unfortunatelly I do not have enough time for that. I need something "condensed" in a single book, and I am trying to find the most suited book for that purpose...

Thank you so much.
 
  • #21
If you're doing this as a hobby, then why does it even matter how much time it takes.

Remember, there is no royal road to geometry. Neither is there one to GR.
 
  • #22
Work, children, etc. You know, I only have a pair of hours a day, as maximum, to study physics. (Besides, you must have noticed that english is not my mother tongue, so I study english as well).

In short, I do not need to master the subject, I am just interested in a rigorous first look to the subject.
 
  • #23
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  • #24
almarpa said:
Work, children, etc. You know, I only have a pair of hours a day, as maximum, to study physics. (Besides, you must have noticed that english is not my mother tongue, so I study english as well).

In short, I do not need to master the subject, I am just interested in a rigorous first look to the subject.

That's the point really. The books you want and the books you're planning to do are not rigorous. If you're ok with that, then no problem.
 
  • #25
Blau's lecture notes (1000 pages!) seem too advanced for me (at the same level tahn Carrol's book, as the author says).I will try to take a look to Martin's book. (I did not know this book, and I am not sure if it is available in my library). If I can't get it, I think I will go with Gron's book.

Thanks all of you.
 
  • #26
atyy said:
I liked Gron's book too.

By the way, as physycist, would you say that this book provides a (more or less) rigorous introduction to GR?

Thanks.
 
  • #27
almarpa said:
By the way, as physycist, would you say that this book provides a (more or less) rigorous introduction to GR?

Thanks.

I'm not a physicist. I'm a biologist who self-studied GR (but I did both biology and physics as an undergraduate, the physics was for fun).
 
  • #28
atyy said:
I'm not a physicist. I'm a biologist who self-studied GR (but I did both biology and physics as an undergraduate, the physics was for fun).

And as a "amateur" physicist?
 
  • #29
almarpa said:
would you say that this book provides a (more or less) rigorous introduction to GR?

Out of curiosity, what does rigour mean to you in this context? Often when I see people talking about rigour, they are referring to mathematical rigour in the sense of a deep, axiomatic-based approach that doesn't gloss over details.

It sounds like you and I have similar self-study goals. It's slow going in my case, but I'm taking a two pronged bottom-up and top-down approach: Following micromass' advice, working my way up through math and in parallel I'm working through physics texts.

I thought I'd point out for a future "next step" it might worth looking into Schultz's "A First Course in General Relativity" both because it's an often recommended/used text and also because I recently noticed there is now a companion book available by Scott called "A Student's Manual for A First Course in General Relativity".

"This comprehensive student manual has been designed to accompany the leading textbook by Bernard Schutz, A First Course in General Relativity, and uses detailed solutions, cross-referenced to several introductory and more advanced textbooks, to enable self-learners, undergraduates and postgraduates to master general relativity through problem solving. The perfect accompaniment to Schutz's textbook, this manual guides the reader step-by-step through over 200 exercises, with clear easy-to-follow derivations. It provides detailed solutions to almost half of Schutz's exercises, and includes 125 brand new supplementary problems that address the subtle points of each chapter. It includes a comprehensive index and collects useful mathematical results, such as transformation matrices and Christoffel symbols for commonly studied spacetimes, in an appendix. Supported by an online table categorising exercises, a Maple worksheet and an instructors' manual, this text provides an invaluable resource for all students and instructors using Schutz's textbook."​
 
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  • #30
micromass said:
Must be a silly book if it does GR without assuming that you're familiar with calculus. Why don't you study up on the math and study GR from an actual good book.
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.
 
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  • #31
vanhees71 said:
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.
 
  • #32
almarpa said:
And as a "amateur" physicist?

Yes, I'm an amateur, which means the only aspect I'm an expert on is quantum interpretations :P
 
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  • #33
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
 
  • #34
vanhees71 said:
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.

atyy said:
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.
 
  • #35
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.
 
  • #36
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.
 
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  • #37
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.
 
  • #38
I am already having problems with these concepts, you see...
 
  • #39
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.
 
  • #40
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.
 
  • #41
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.
 
  • #42
Ok, I will take a look Schutz book as well. I think I saw it at the library.

Tanks for the advice.
 
  • #43
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.
 
  • #44
almarpa said:
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.
 
  • #45
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?
 
  • #46
ibkev said:
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/
 
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  • #47
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.
 
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  • #48
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.
 
  • #49
almarpa said:
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).
 
  • #50
Just curious, what was your roadmap to learn general relativity?
 

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