Introduction to GR. ¿Gron or Collier?

[almarpa]

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.

 

[vanhees71]

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.

 

[almarpa]

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?

 

[smodak]

Both are equally good - see the previews in Amazon / Springer website and pick the one you like better.

 

[ibkev]

Do either of these books assume you understand calculus of variations or lagrangians?

 

[smodak]

Do either of these books assume you understand calculus of variations or lagrangians?

No

 

[almarpa]

No. Both them consider you could even not be familiar with calculus.

 

[micromass]

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.

 

[smodak]

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.

 

[micromass]

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.

 

[almarpa]

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.

 

[smodak]

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.

 

[micromass]

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.

 

[micromass]

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.

 

[smodak]

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.

 

[almarpa]

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.

 

[micromass]

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.

 

[almarpa]

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

 

[micromass]

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.

 

[almarpa]

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.

 

[micromass]

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.

 

[almarpa]

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.

 

[atyy]

I liked Gron's book too.

Before Gron I read J. L. Martin's General Relativity: A First Course for Physicists
https://www.amazon.com/dp/0132911965/?tag=pfamazon01-20

Collier's book seems very interesting. I'd love to take a look at it.

To save money, you can try
http://www.blau.itp.unibe.ch/newlecturesGR.pdf
http://sms.victoria.ac.nz/foswiki/pub/Courses/MATH465_2016T2/WebHome/AAA-notes-465-2016.pdf

 

[micromass]

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.

 

[almarpa]

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.

 

[almarpa]

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.

 

[atyy]

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).

 

[almarpa]

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?

 

[ibkev]

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."​

 

[vanhees71]

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.

 

[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.