Looking for a good book on GR

[Peter99]

Hello,

I would like to better understand the geometric evolution of a gravitational field of a simple point mass as the velocity difference between two different inertial frames approaches the speed of light. I would also then like to extend into more complex scenarios such as charged particles.

This takes me directly to General Relativity and Einsteins Field Equations.

So I am looking for a book that will robustly cover these subjects. I think it should start at the undergraduate level but it would be OK if it then went into graduate level. Note that my only resources will be the books that I have and the good people on this forum so if the book is too abstract that may be a problem but then again, if the book is too "dumbed down" then it may not get me to where I want to go. So I'm looking for a good balanced book. If this cannot be achieved with one book, then two books is OK.

Thanks for the help and suggestions,
peter99

 

[jedishrfu]

Physics stack exchange had a similar discussion with many good books listed:

http://physics.stackexchange.com/questions/363/getting-started-self-studying-general-relativity

My preference is the dated Wheeler Misner and Thorne book. It had great pictures and diagrams.

A more recent book is Einstein Gravity in a Nutshell by Zee that is considered to be the best so far.

http://press.princeton.edu/titles/10038.html

 

[vanhees71]

My favorite as a starting point is Landau&Lifshitz. Misner, Thorne, Wheeler is also very good, but pretty intimidating with introducing the Cartan calculus right away. I don't know Zee's book at all, but if it is like the QFT book, I cannot recommend it.

 

[ShayanJ]

I think Zee's book is very nice to begin with(Its not like his QFT book or, to be precise, its like his QFT book, its just that his method is proper for GR but not for QFT). Then you can start reading Padmanabhan's Gravitation to get a more advanced understanding.

My honorable mention goes to Schutz's "A first course in General Relativity".

 

[Peter99]

Excellent! These are great suggestions and the links provided were very helpful.

It seems that not one, not two, but four books are in the running here. Let me see if I understand this correctly:

For a good, solid, thorough presentation of GR, although perhaps slightly "outdated in emphasis", the books from authors

1) Landau & Lifshitz
2) Misner, Thorne, Wheeler

are good to have. I even saw a comment that Misner, Thorne, Wheeler was almost considered the "Bible" of GR.

If I want a more current presentation of GR then

3) Zee
4) Padmanabhan

should be considered. Also, Padmanabhan seems to cater to self studies and seems to have arranged the book with this in mind.

Dr. Michael Dine (from UCSC) had this comment about Zee:

"...it is an excellent complement to Hartle's book and good preparation for Carroll's."

I took a couple of courses from Dr. Dine and I do respect his opinions (really nice guy too!). Can anyone comment more completely on where the books 5) Hartle and 6) Carroll would fit in with the four books mentioned above?

Thanks again for the input and insight,
peter99

 

[Peter99]

My favorite as a starting point is Landau&Lifshitz.

What did you like about this book as a starting point? Does it ease into things nicely?

-peter99

 

[Peter99]

Then you can start reading Padmanabhan's Gravitation to get a more advanced understanding.

Padmanabhan makes a (what I consider to be odd) comment in his preface that:

That "most of the existing books on the market are either outdated in emphasis, TOO MATHEMATICAL FOR PHYSICISTS, ...etc."

The odd comment being "too mathematical for physicists". Does anyone else find this odd? I mean, what exactly is too mathematical for physicists?

peter99

 

[George Jones]

Padmanabhan makes a (what I consider to be odd) comment in his preface that:

That "most of the existing books on the market are either outdated in emphasis, TOO MATHEMATICAL FOR PHYSICISTS, ...etc."

The odd comment being "too mathematical for physicists". Does anyone else find this odd? I mean, what exactly is too mathematical for physicists?

From Zee's book:

I am certainly not against coordinate-free notations ... Coordinate-free notations are great for proving general theorems, but not so good for calculating ...chatting at lunch with two leading young researchers ... During grad school, to deepen his understanding of Einstein gravity, he enrolled in a course taught by a famous mathematician. As it happened, he was the only student able to do the problems in the final exam involving actual calculations: he did them by first using old-fashioned indices and then translating back into the abstract notation used in the course.

This was a physics student enrolled in a pure math grad course. Even math grad students can have trouble doing calculations in a coordinate-free manner!

I personally find that coordinates can be useful for calculation, and that coordinate-free notation often is useful conceptually, although these aren't completely general statements.

 

[smodak]

The best book that eases you into it is https://www.amazon.com/dp/0805386629/?tag=pfamazon01-20 -a wonderful book.

 

[vanhees71]

What did you like about this book as a starting point? Does it ease into things nicely?

-peter99

Vol. 2 of Landau Lifshitz for me is among the best books to introduce to classical field theory. Particularly electrodynamics is presented in a modern way and not another copy of a 19th century textbook with some last chapter about relativity. In my opinion theoretical physics should introduce special relativity at the end of the mechanics lecture and then electrodynamics should be taught right away as a relativistic field theory. Concerning GR Landau and Lifshitz come quickly to the point, and the arguments are physics rather than a long chapter on differential geometry. Of course, you also get the differential geometry you need to understand the physics.

There are of course tons of other good books on GR (in fact I don't know any I'd really discourage to read; I've many more objections, sometimes even aversions as in the case of Zee's "QFT in a Nutshell", against some QM and QFT books). Another very good book is Weinberg's Gravitation and Cosmology although concerning cosmlogy it's outdated. He has also written a new book on cosmology. However, Weinberg's textbooks are generally not to start with a subject but to get all the subtle details later. Padmanabhan's book is somewhere in between.

 

[Peter99]

This was a physics student enrolled in a pure math grad course. Even math grad students can have trouble doing calculations in a coordinate-free manner!

Yes, exactly! So per my implied point, I don't think there is any math that is ultimately too complicated for a physicist! I mean, I don't want to sound too uppity here where physicists are concerned but I just don't see any math being too complicated for a physicist. So this is why the comment by Padmanabhan just sounded odd to me. Maybe I just didn't understand what he meant.

The best book that eases you into it is https://www.amazon.com/dp/0805386629/?tag=pfamazon01-20 -a wonderful book.

Thank you for that! I'll add this book to my list.

Vol. 2 of Landau Lifshitz for me is among the best books to introduce to classical field theory. Particularly electrodynamics is presented in a modern way and not another copy of a 19th century textbook with some last chapter about relativity. In my opinion theoretical physics should introduce special relativity at the end of the mechanics lecture and then electrodynamics should be taught right away as a relativistic field theory. Concerning GR Landau and Lifshitz come quickly to the point, and the arguments are physics rather than a long chapter on differential geometry. Of course, you also get the differential geometry you need to understand the physics.

There are of course tons of other good books on GR (in fact I don't know any I'd really discourage to read; I've many more objections, sometimes even aversions as in the case of Zee's "QFT in a Nutshell", against some QM and QFT books). Another very good book is Weinberg's Gravitation and Cosmology although concerning cosmlogy it's outdated. He has also written a new book on cosmology. However, Weinberg's textbooks are generally not to start with a subject but to get all the subtle details later. Padmanabhan's book is somewhere in between.

Some sage advice here for sure! Great input! :) Now I just have to decide which book/s to start with. I've never actually had a specific course in GR. It was always entitled "Modern Physics" or some such which usually included a few chapters on special relativity. I think this is why I am a bit hesitant on which book to start with. I think I got the basics though and now I really want to get into the serious nuts and bolts of GR. But I love books and I love just going somewhere without WiFi or a computer or a tablet and holding a good book in my hands with a pen (yes, I prefer pens! I always got teased because I used a pen on tests/homework rather then a pencil), a calculator, and a pad of paper and getting into it! So I think I'm just going to buy at least two, maybe even three! Anyway, I digressed here a bit. Thanks for the input and off to Amazon I go (through PF of course - 6% to PF right?)!

 

[smodak]

Jennie Traschen reviewed Hartle's book on Physics Today 58(1), 52 (2005); doi: 10.1063/1.1881902. Below is an excerpt. I find the review spot on.

Jim Hartle’s Gravity is a gem that offers a novel approach to general relativity pedagogy. It is written for senior level undergraduate physics students, but I expect it will be useful for a broader audience. The writing throughout is clear, methodical, and elegant, spiced with the author’s characteristic dry sense of humor. Hartle’s strategy is not to start, in the usual way, with the definition of a manifold and the development of differential geometry. Instead, the bulk of the text uses only calculus and basic differential equations; a streamlined treatment of differential geometry is given at the end of the text. The primary analytical tools developed are how to extract information from metrics and how to study geodesic motion in a given spacetime. Geodesics and Christoffel symbols are introduced using Lagrangian techniques. Given a spacetime metric, the primary analytical tools are then sufficient for extracting an enormous amount of interesting physics. Key concepts, such as the notion of invariant geometrical quantities that underlie the differential geometric formalism of general relativity, are presented early on. The text begins with the best nuts-and-bolts discussion of gravity as spacetime geometry that I have seen. That discussion enables students to take on the presented calculations with a “full GR attitude.” Hartle’s reversal of the usual ordering of a general relativity syllabus takes some getting used to, but it offers the potential for real success. Instead of struggling through the first half of the course to get to the Einstein equation, many students—undergraduate and graduate—are likely to develop a better grasp of the physics of general relativity, and how to extract it from basic calculations with the spacetime metric, through Hartle’s method. Hartle’s textbook makes an interesting read, even for more senior relativists. It is packed with calculations of observable general relativistic effects and accompanied by excellent diagrams and descriptions of actual experiments. The author takes calculations one step further than most general relativity texts and gives the reader the physics punch line. One such example concerns unbound orbits in the Schwarzschild geometry. First, readers are led through the routine analysis of particle motion in the relativistic potential. Then sample orbits are displayed as two dimensional plots. In one picture, a massive particle comes in from infinity, completely loops the central mass (crossing its own path), and heads off to infinity. Such behavior is very non- Newtonian! Another example that comes to mind (perhaps because gyroscopes seemed so confusing in first year physics) is the clear calculation of the precession of a gyroscope in the field of a slowly rotating body. That example includes a short discussion about NASA’s Gravity Probe B. The chapters on cosmology are excellent and include a survey of current observations, especially useful for those of us who need to update our cosmology notes. The diagrams and plots in these chapters are densely packed and useful.

Hartle does not omit steps and derives everything. The book is written in such a way it is very engaging and interesting to read and full of physical insights. In my opinion this is how Physics books should be written.

 

[martinbn]

Padmanabhan makes a (what I consider to be odd) comment in his preface that:

That "most of the existing books on the market are either outdated in emphasis, TOO MATHEMATICAL FOR PHYSICISTS, ...etc."

The odd comment being "too mathematical for physicists". Does anyone else find this odd? I mean, what exactly is too mathematical for physicists?

peter99

I think "too mathematical for physicists" means that they (the physicists) consider the text to be concerned with topics that are of only mathematical interest that doesn't help the understanding of physics. For example how often do physicists read Chrisodoulou or Klainerman's papers?

 

[Demystifier]

I think "too mathematical for physicists" means that they (the physicists) consider the text to be concerned with topics that are of only mathematical interest that doesn't help the understanding of physics. For example how often do physicists read Chrisodoulou or Klainerman's papers?

What is your favored book on GR?

 

[martinbn]

What is your favored book on GR?

Hard to tell. I like Wald, Geroch's lecture notes, and some others.

 

[Demystifier]

Hard to tell. I like Wald, Geroch's lecture notes, and some others.

Good, I was afraid that you will mention some more abstract mathematical texts such as Sachs and Wu.

 

[martinbn]

Good, I was afraid that you will mention some more abstract mathematical texts such as Sachs and Wu.

Well, I like Sachs and Wu too, but I thought you mean physics books.

 

[Demystifier]

Well, I like Sachs and Wu too, but I thought you mean physics books.

Well, Sachs and Wu is "GR for Mathematicians", so it can be categorized as physics book written for mathematicians. What I really want to know is what do you like more, books like Wald or books like Sachs and Wu? Or perhaps you like them at different levels, so that it cannot be compared?

 

[martinbn]

Ah, well, I like Sachs and Wu's style more, even better is the book of O'Neil, but that is a geometry book. But I like Wald more because he covers more topics.

 

[smodak]

Well, Sachs and Wu is "GR for Mathematicians", so it can be categorized as physics book written for mathematicians. What I really want to know is what do you like more, books like Wald or books like Sachs and Wu? Or perhaps you like them at different levels, so that it cannot be compared?

What I really want to know is, would Einstein have liked Wald's book? :)

 

[Demystifier]

Ah, well, I like Sachs and Wu's style more, even better is the book of O'Neil, but that is a geometry book. But I like Wald more because he covers more topics.

Well, O'Neil has two books I am aware of. One of them is a physics book: The Geometry of Kerr Black Holes.

 

[martinbn]

Well, O'Neil has two books I am aware of. One of them is a physics book: The Geometry of Kerr Black Holes.

I like that one too. I meant the semi-riemaniann geometry one.

 

[The Bill]

Misner, Thorne, and Wheeler's Gravitation was mentioned earlier in the thread. I'd like to point out that it's being reprinted in hardcover, and will be available on the 9th of this month, this coming Monday:

https://www.amazon.com/dp/0691177791/?tag=pfamazon01-20

 

[Demystifier]

Misner, Thorne, and Wheeler's Gravitation was mentioned earlier in the thread. I'd like to point out that it's being reprinted in hardcover, and will be available on the 9th of this month, this coming Monday:

https://www.amazon.com/dp/0691177791/?tag=pfamazon01-20

Good timing, just after one of the authors got the Nobel prize. Remarkably, another book by that Nobel prize winner has been published a couple of weeks ago. Is it just a coincidence, or did publishers count on it that he could get the Nobel?

 

[The Bill]

Good timing, just after one of the authors got the Nobel prize. Remarkably, another book by that Nobel prize winner has been published a couple of weeks ago. Is it just a coincidence, or did publishers count on it that he could get the Nobel?

Since they're both textbooks, I think it's probably a coincidence.

If a publisher wanted to cash in, they'd make an inexpensive popular science book. Thorne hasn't published one of those since 2014.

 

[vanhees71]

Even better, I guess they now will bring out more DVDs etc. of the movie "Interstellar" as "adviced and produced by a Nobel Laureate" :-)).

 

[smodak]

Even better, I guess they now will bring out more DVDs etc. of the movie "Interstellar" as "adviced and produced by a Nobel Laureate" :-)).

https://www.amazon.com/dp/B00S00NYW8/?tag=pfamazon01-20
https://www.amazon.com/dp/0393351378/?tag=pfamazon01-20