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Relativity Another General Relativity book thread

  1. Aug 27, 2015 #1

    Apologies; In spite of the numerous excellent threads that exist discussing GR books, I felt compelled to create another one.

    I'm taking a first course in GR & Cosmology, and am trying to select a textbook as the main 'roadmap' through GR. This is a first course on GR in the UK, which is equivalent to the first grad course on GR in the US. I already know special relativity using 4-vectors and the covariant formulation of classical electromagnetism, but wouldn't mind a good repeat review at all.

    I have narrowed my choices to the following books:
    1. R. D'Inverno - Introducing Einstein's Relativity (currently my choice as main text)
    2. S. Carroll - Spacetime & Geometry: Introduction to GR (choice as a companion to D'Inverno)
    3. B. Schutz - A First Course in General Relativity (may replace Carroll as a companion to D'Inverno)
    4. J. Callahan - The Geometry of Spacetime: Intro to SR & GR (have heard a lot of good things about this)
    5. A. Zee - Einstein Gravity in a Nutshell (which apparently is MUCH better than the bad QFT Nut)
    6. L.D. Landau - Classical Theory of Fields (This is here for the sole reason that I love Russian texts)

    Other available options that I don't feel too strongly about (but perhaps you could change my mind?):
    1. L. Ryder - Introduction to General Relativity
    2. J. Hartle - Gravity: An Introduction to Einstein's General Relativity
    3. R. Lambourne - Relativity, Gravitation, and Cosmology
    4. N.M.J. Woodhouse - General Relativity
    5. P.A.M. Dirac - General Relativity
    6. S. Weinberg - Gravitation & Cosmology
    7. R.M. Wald - General Relativity
    8. MTW - Gravitation
    9. Hans Stephani - General Relativity: An Introduction to the Theory of the Gravitational Field
    Note: Some books in the second list above are first rate classics, but are inappropriate for a first course, or are too encyclopaedic to serve as textbooks.

    I'm looking for a textbook that develops the mathematical formalism that it uses, and strikes a balance between mathematical rigour and the physics. I don't mind heavily mathematical or verbose treatments (they usually tend to be more pedagogic).

    If people would care to comment on and compare the books above, or suggest new books, that would be fantastic. Please feel free to suggest combinations of books (that go well together), and also auxiliary leisure reading to accompany the course proper.

  2. jcsd
  3. Aug 27, 2015 #2


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    Among those you listed my favorites are Landau-Lifshitz vol. 2, Weinberg, Stephani. Also Dirac is great, because it's so brief, but maybe that's not so good to begin with just for that reason. If you want to learn more modern concepts like the Cartan calculus, MTW is of course also great. A very good free-of-charge online resource are Blau's lecture notes:

  4. Aug 27, 2015 #3


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    Perfect for a first study.
    And as a second study, I recommend Gravitation by Padmanabhan. This is a very nice book and you can't replace it with any of the above.

    EDIT: I also recommend you to read Special Relativity in General Frames by Eric Gourgoulhon even if you already know some SR.
    Last edited: Aug 27, 2015
  5. Aug 27, 2015 #4
    Thanks for the recommendations. Just looked at those lecture notes, they seem very good on a first read and the table of contents made me gasp. I suppose they're too extensive to be used alongside a lectured course, but would make a fantastic reference or the focus of concentrated summer study.

    I'm told Weinberg is his usual self in 'Gravitation & Cosmology', going against the norm in treatment and notation. No doubt it is a must-read and full of insight, but again would complicate things when used to complement a lecture course.

    Landau is fantastic as a writer, but I've seen people saying Vol.2 (CFT) is dated. Same goes for Dirac's GR (he covers it in a blinding 70 pages). I've peeked at Stephani, which seems very good, covering quite a bit of maths and physics in detail (compared to contemporaries) in a reasonable number of pages.

    It's just so difficult to arrive at a final choice of textbook(s) that can be read under the stress and time-limits due to other courses at uni. Some books require several hours of concentrated effort to break though a few pages, whereas others read like a breeze.

    I've heard that this one is quite good. I've looked at QFT Nut, and I confess I didn't like it very much. I switched to studying QFT using a combination of D. Tong's lecture notes & videos, Timo Weigand's FANTASTIC lecture notes from his courses at Heidelberg uni, Peskin & Schroeder, and the occasional peek at MD Schwartz, M.Srednicki.

    But I've heard Zee's GR book is fantastic. Will it serve well alongside a traditional course in GR? How much and what maths does he use? Does it compare to the level of Carroll?

    P.S. I recall Padmanabhan's book being listed on amazon, but i haven't had the chance to have a peek yet. Will definitely have a look.
  6. Aug 27, 2015 #5


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    Actually I just started learning QFT. The main text I'm reading is Schwartz's "Quantum Field Theory and Standard Model". But I read some chapters from "Quantum Field Theory for Gifted Amateur" by Lancaster and Blundell and "Quantum Field Theory of Point Particles and Strings" by Hatfield. I also read some chapters from "Introduction to Quantum Effects in Gravity" By Mukhanov and Winitzki(Very nice book). They all helped to make me feel better about QFT. I plan to read Weinberg's book in near future.

    Yes, its fantastic.
    I don't think its that much compatible with a traditional course on GR.
    You only need calculus for understanding it. It develops all the math that is needed.
    I think its only a bit below Carroll.
    Now that you want a course compatible book, I think D'Inverno's is your best choice. And if you read Padmanabhan's after that, you'll have a good understanding of GR.
  7. Aug 27, 2015 #6


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    Hm, at least concerning the classical electrodynamics part I think to the contrary that Landau's book is one of the few which is up to date enough, to treat electromagnetism as a relativistic theory right from the beginning as it should be done, because you save yourself from many mind-boggling apparent paradoxes when treating E+M semi-nonrelativistically, particularly when it comes to macroscopic electrodynamics. Concerning the GR part, I don't know what's outdated. It uses exclusively the Ricci calculus. Maybe that's outdated for practioners in GR, because they may use the Cartan calculus, but that doesn't make a introductory textbook outdated. For sure what's outdated are the cosmology parts, although of course the foundations are also covered quite well. The Friedmann-Lemaitre-Robertson-Walker solutions are still the basis of cosmology. For cosmology you anyway need a very modern text to be up to date, e.g., Weinberg's Cosmology (2008).

    Weinberg's GR book (1971) is great, because it's a physicist's rather than a geometer's book.

    Of course, if you use the book in parallel to a lecture, you better take the book recommended by the professor, because it can be confusing to learn a subject from different point of view from the very beginning. Of course, one should get such broader views but it's better to have one coherent presentation to start learning a subject.
  8. Aug 28, 2015 #7
    Weinberg is the final 'test of adulthood', I suppose. I'm still a lowly 2nd year undergraduate. One more round through Peskin or Schwartz or one of the 'how to do feynman diagrams' books and then I'll attack Weinberg. I initially read a little from Lancaster & Blundell, but the chapters were too short and I noticed a few topics were left out. But there are some snippets in that book, especially the sidenotes and the occasional solid state section that I like. I haven't seen the other two books that you mention; I'll add them to my 'peek list' on the next visit to a bookstore. The most helpful resource has been Timo Weigand's lecture notes (linked). He uses Peskin as a roadmap, but he adds 'extra' delightful comments here and there, and in some places decides to do things differently that I'm yet to come across in any textbook. These 'alternate' methods appeal very much, I think, to NRQM intuition. I'm also looking through R. Klauber's Student-Friendly Quantum Field Theory', which also seems superbly written (except for the horrible typesetting).

    Zee has some exotic topics in the end, which will make it an entertaining summer read. There's a copy in my university library, so I think I'll pick out and read random sections from it instead of 'working through it'. I don't have access to Padmanabhan's book, but I used the 'look inside' feature on amazon, and oh my! It looks like it has everything and more (last chapter is 'Gravity as an emergent phenomenon'). Thanks for this; it'll definitely be my second read once I get the foundations nailed down.

    I have read the first two chapters (SR) of Landau's CFT, and they were food for the starved soul after a trip through the usual barns and ladders and trains approach (which have their place, I suppose). I became apprehensive of the GR sections after I read a few negative reviews, but after your comment I rapidly compared D'Inverno and Landau, and they seem similar in the maths (although D'Inverno has a lot more extra topics). Thanks for clearing that up.

    But doesn't the GR frontier exclusively use the geometric approach? All the discussions on GR books that I've come across acknowledge Weinberg's (1971) book as a classic (of course they would, he's a nobel laureate), and recommend it as one of those 'aside readings', or 'insights into a master physicist's thinking'. But they also proclaim the methods in the book as obsolete.
  9. Aug 28, 2015 #8
    In the end, I've decided to rapidly sprint through Dirac's GR "pamphlet" before the course starts and absorb what I can. Then, I'll use a combination of D'Inverno (recommended text) and Landau's CFT for the course itself. I'll also perhaps have an occasional glance at Carroll (or Zee) to pick out any special topics if time permits.

    P.S. Actually, THE best discussion on the tensor calculus and algebra that I've read comes from Linear Algebra and Multidimensional Geometry by N.V. Efimov and E.R. Rozendorn. Starts out with elementary linear algebra and then takes one right up to hypersurfaces (in 350 small pages), and hits the sweet spot between theory and application. Much like Landau in writing style - concise, not a single letter on the page goes waste.
  10. Aug 28, 2015 #9


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    Ok, I'm not an GR expert, and it might be that that's why I love Weinberg's book (as all of Weinberg's books by the way) so much. Of course, the argument that somebody is a Nobel laureat doesn't tell you anything about his textbook-writing abilities. There are Nobel-prize winners who don't write very clear papers or books (the worst for me are Bohr and Heisenberg, and the latter has written papers in my mother tongue, German ;-)). Others are of course also great writers (in fact the majority of them; in German examples are Einstein, Pauli, von Laue, Born; in English Dirac, Feynman, Weinberg).

    What I don't understand is the remark that Weinberg's methods in his GR book are obsolete. In which sense? The math is not so different from the other textbooks using Ricci calculus. So what's obsolete with that? As I said, I'm not an expert in GR.

    Most recently I got the books by Padmanabhan, which I think is a good book to start with too and by Straumann, which is very advanced and a bit hard to read for a non-expert.
  11. Aug 30, 2015 #10
    Straumann is more advanced than Padmanabhan? Padmanabhan states in his preface that he's included topics that haven't found their way into any other textbooks yet. He also suggests the use of the book as a reference for active researchers in the field. I thought that book was the grand finale for textbook learning in GR, after which only papers could provide more information. Is Straumann more mathematically sophisticated?

    I haven't learned GR at all yet, so I'm just trying to get a review of the literature on the subject from people who know more.

    EDIT: Also, has Wald's classic been superseded in usage by other books like those mentioned above?
  12. Aug 31, 2015 #11


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    I think Padmanabhan is indeed very advanced. I like it very much, and although I'm not an expert or in research with GR/Cosmology I find it very well understandable, while Straumann is more sophisticated in his math, but that's perhaps also subjective, because I'm used to the Ricci index calculus and not so familiar with the Cartan calculus of forms.
  13. Aug 31, 2015 #12


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    I searched for "Ricci calculus obsolete" in Google and didn't find a single result or discussion where it was even mentioned that that might be the case. Certainly people would be talking about it if was because people always want to jump ship when there is something new.
  14. Sep 4, 2015 #13
    Apologies, perhaps obsolete is the wrong word to use. But dated and idiosyncratic. Neil Turok, in one of his PSI lectures on relativity, says something along those lines. Padmanabhan, whose book has been discussed above, also says so in the first of a series of lectures on relativity on youtube. Even though one don't see devoted discussions on the topic, there's a culture associated with a certain book that one senses.

    I personally have not read GR yet, but from what I've learned in hunting for resources on GR, Weinberg's book is 'different', but is a great read. I was merely trying to find the reason why it wasn't used in courses, and found people commenting on its idiosyncratic notation and non-geometric treatment. Here is a discussion that I recently found on the topic, although I haven't yet read all the posts in full.

    Thanks for the reply. Padmanabhan sounds like a good follow up to a standard introduction to GR. People also seem to recommend O'Neill's Semi-Riemannian Geometry with Applications to relativity, as a proper mathematical introduction to GR. There's an interesting Amazon.com review of this book by "A Reader", who recommends O'Neill's book as a first book on GR.
  15. Sep 4, 2015 #14


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    Hm, as I said already above, I find it speaks for Weinberg being not geometric. There are enough very good GR books emphasizing the geometric point of view. So it's good that there is a physics-emphasizing approach too. The point of all of Weinberg's books is that they follow a different approach than others, and it's always an approach that makes the physics concepts very clear, while using exactly the mathematics you need to achieve this clarity. Every textbook I've seen written by Weinberg is a masterpiece.
  16. Mar 24, 2016 #15
    It's been almost six months since I posted this thread. This is an update.

    I started out with D'Inverno as that was prescribed as the course text but I dropped it after the first week (after reading the chapter on tensor calculus). It's a classic example of how not to write a physics textbook. The mathematics is laid out before the physics with great obscurity and with zero motivation. Although I do love mathematics in its purest form, I'm training to become a theoretical physicist and when I read physics, I expect to see some physical motivation for the use of a particular choice of mathematical model. In the case of QM, it's the use of vector spaces. In GR, it's the use of tensors and differential geometry etc. Inverno neither physically motivates nor explains well the mathematical formalism underlying GR.

    I ended up using a combination of Classical Theory of Fields by L&L (Vol.2) and Gravitation: Foundations & Frontiers by T.Padmanabhan, and the result was without exaggeration one of the greatest experiences of my life. The latter is in fact a superb modern update of the former (as someone else on physicsforums stated). Both books pay due homage to the variational principle and show how powerful it truly is.

    Every bit of mathematics used is physically motivated. The books show how the physics so naturally suggests the mathematical model. For example, the books contain:

    1. A clear exposition of the reason why gravitational effects can be reinterpreted as geometry and encoded in the metric.

    2. An amazingly simple argument showing that a general metric can be locally reduced to the Minkowski metric and have first (but not higher) derivatives set to zero via a local coordinate transformation.

    3. Imposing general covariance on physics leads to the geodesic equation and concept of a covariant derivative (via action principle). Although physics-motivated, the geometrical meaning of these concepts are also carefully explained in Padmanabhan.

    4. Concept of Killing equations and fields is shown to be required under spacetime symmetries and conservation laws.


    The first half of Padmanabhan's book is an introductory exposition of classical electrodynamics (done the sensible way through the action principle) and general relativity, while the second half contains some fairly advanced specialised topics in gravitational physics (including a recasting of GR in the abstract, coordinate-free form). His arguments are very similar to those of Landau and dare I say, clearer and more refined. The problems and more importantly, the projects in Padmanabhan's book are also a priceless addition to the text.

    In summary, I stand in awe of the physical intuition of both authors and I fervently recommend the combination of L&L and Padmanabhan to anyone who wishes to study GR, introductory or advanced.

    P.S. Padmanabhan has also very recently published an 'introductory' book on QFT emphasising the path integral approach and the Wilsonian perspective of renormalization from the very beginning. It would be great if someone conversant in the subject could take a look and post a review here - https://www.physicsforums.com/threa...the-why-what-and-how-by-t-padmanabhan.862963/
  17. Mar 24, 2016 #16


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    I've looked at Padmanabhan's QFT book only superficially, but I'm not too enthusiastic about it. At the moment my favorite introductory QFT textbook is

    Schwartz, M. D.: Quantum field theory and the Standard Model, Cambridge University Press, 2014
  18. Mar 26, 2016 #17
    Carrol is a Wald just more didatical, Carrol says that in the firsts pages of the book.Carrol's book is very mathematical,I like it but is hard for a beginner.
    Landau is the best book for a first introduction in fields.
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