1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential Geometry for General Relativity

  1. Nov 28, 2007 #1
    Please recommend some good books of differential geometry for a physics student.

    Thanks!
     
  2. jcsd
  3. Nov 28, 2007 #2

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  4. Nov 28, 2007 #3
    Physics books typically jump right into Riemannian geometry without discussing e.g. local surface theory. A couple books for background that will help give you a more intuitive feel for the math:

    http://www.amazon.com/Riemannian-Geometry-Beginners-Frank-Morgan/dp/1568810733/
    http://www.amazon.com/Differential-Geometry-Relativity-Theory-Introduction/dp/082471749X

    I still like Schutz, even though his emphasis is not Riemannian geometry:

    http://www.amazon.com/Geometrical-Methods-Mathematical-Physics-Bernard/dp/0521298873/

    Frankel is pretty readable and covers an interesting selection of topics:

    http://www.amazon.com/Geometry-Physics-Introduction-Second/dp/0521539277/

    An older text, Bishop & Goldberg, is pretty concise, but I like it for that and the price is right:

    http://www.amazon.com/Tensor-Analysis-Manifolds-Richard-Bishop/dp/0486640396/
     
  5. Nov 28, 2007 #4

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If the goal is to understand relativity, I would first seek out treatments of differential geometry by a mathematically-oriented relativist... then to others when needed.

    Some names (in no particular order... some found in the URL I pasted above):
    Schutz, Faber, and Frankel (as named above)
    Burke, Isham, Sachs&Wu, O'Neill, Crampin, Marsden, Choquet-Bruhat, Hawking&Ellis, ....

    http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf

    edit:
    add Szekeres
    see also https://www.physicsforums.com/showthread.php?t=168568
     
    Last edited: Nov 29, 2007
  6. Nov 29, 2007 #5
    I am reading Frankel's book. But it is the first edition. Is the change between the first edition and the second edition very big and significant?
     
  7. Nov 29, 2007 #6

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I don't have the editions on hand to compare....
    however, the Amazon review (from the URL above) says
    "Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact Lie groups."
    Based on that, it seems that:
    for applications to GR, I think the second edition covers as much as the first.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?