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Which text on differential geometry to supplement relativity

  1. Sep 2, 2015 #1
    I am looking to pick up one of these texts, but I don't really want to buy all three. Is there a considered favorite? Thanks in advance.

    B. O'Neill: Semi-Riemannian Geometry with Applications to Relativity

    T. Frankel: The Geometry of Physics

    B. Schutz: Geometrical Methods of Mathematical Physics
     
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  3. Sep 2, 2015 #2

    vanhees71

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  4. Sep 2, 2015 #3

    robphy

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    It depends.
    Those three focus on different topics and will appeal to different audiences. What kind of relativity course of study are you pursuing?
    What relativity text are you using?
     
  5. Sep 2, 2015 #4

    bapowell

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  6. Sep 2, 2015 #5
    robphy: I am refreshing my E&M / SR with Ohanian's E&M text. I want to study GR and have several books - Schutz (old edition - small green paperback), D'Inverno, Weinberg, Ohanian-Ruffini, Dray and Zee. I was planning to read Weinberg first to get "to the physics" as quickly as possible.

    I have a PhD in math but in analysis and number theory. My background in geometry and topology is weak, but I am generally good with proofs and mathematical "maturity". I was considering getting a supplementary text as noted above, since I find I often sidetrack myself to put the math on solid footing if the physics text doesn't do so. Thanks.
     
  7. Sep 2, 2015 #6

    Ben Niehoff

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    I'm partial to Nakahara, especially if you're comfortable with a more "mathy" treatment.
     
  8. Sep 2, 2015 #7

    robphy

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    For a supplement to relativity, I would prefer a book that made explicit connections with relativity.
    "How can mathematics be used to model the physics?"

    The three books you listed are written by mathematically-oriented relativists
    It's difficult to pick one.
    I offer my opinions as a physicist interested in geometrical formulations.

    If the focus is relativity, I would choose
    B. O'Neill: Semi-Riemannian Geometry with Applications to Relativity
    or
    F. de Felice & C.J.S. Clarke: Relativity on Curved Manifolds

    If the focus is relativity and other physical topics, I would choose
    T. Frankel: The Geometry of Physics (who also has a small book called Gravitational Curvature )
    or
    P. Szekeres: A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry

    B. Schutz: Geometrical Methods of Mathematical Physics
    would be good as an overview... but you might find yourself looking elsewhere for more details.

    I admit that I'm not so comfortable with Nakahara.


    You might find these useful:
    http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf
    https://projecteuclid.org/euclid.bams/1183539848 (article by Sachs & Wu., who also have an old book "General Relativity for Mathematicians")
    http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html
     
  9. Sep 3, 2015 #8

    haushofer

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    I'm a Nakahara-fan :P But a text like Carroll also gives sufficient background info, I guess. Btw, I absolutely love Zee's book. It's big, but a fun read full of surprising insights and topics!
     
  10. Sep 3, 2015 #9

    ShayanJ

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    Several of reviews on amazon say that Nakahara has too many typos. Are they very bothering?(I mean the typos!)
     
  11. Sep 3, 2015 #10

    haushofer

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    Not really. I didn't have the impression is was so bad.
     
  12. Sep 3, 2015 #11
    I like Schutz, it's pretty basic, but well done. I also think it's better oriented towards physics. I think it's a little too basic to make it you're only text, but I guess it depends on what you're looking for as an end goal. I think Frankel is good, but I found it to be a bit idiosyncratic. As a math person you might like it better though. I don't know O'Neill, so can't comment on how that compares.
     
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