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Tensor calculus for general relativity

  1. Mar 18, 2010 #1
    I'm taking a course on relativity, both special and general. According to my college, I have the required mathematical background (vector analysis, electromagnetics (though I can't recall more than a cursory glance at tensors) etc) to make sense of it. Special relativity I can handle, and I think I understand the general concepts of GR fairly well, but how to actually do the math eludes me.

    The book I have is Ta-Pei Cheng's Relativity, Gravitation and Cosmology. It does an OK job of explaining the theory, but it tends to not do the calculations, instead calling them 'straight forward'. Math has, sadly, never came that naturally to me, and I don't follow. So what I need would be a guide to the mathematical framework, one that spells it all out explicitly. Does anyone have any recommendations?
  2. jcsd
  3. Mar 18, 2010 #2


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    Misner, Thorne, and Wheeler is the classic reference on GR, and it explains tensor calculus from several different viewpoints, so it might be a good reference.
  4. Mar 18, 2010 #3
    Some online sopurces....

    Some Caltech notes:

    And from Benjamin Crowell of this forum:
    http://www.lightandmatter.com/html_books/genrel/ch04/ch04.html [Broken]

    And from John Baez,

    And from Hofstra,
    http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html [Broken]

    And from mathpages, around 5.2:

    Good luck..I collected some references but have not studied them due to time constraints so I can't recommend one over another.
    Last edited by a moderator: May 4, 2017
  5. Mar 19, 2010 #4
    Sean Carroll's Lecture Notes on General Relativity can also be found here, along with a condensed version and some further resources.

    Kip Thorne & Roger Blandford: Applications of Classical Phyisics

    Kip Thorne also has a series of video lectures online about gravitational waves, which include an introduction to tensor analysis.

    I found the following book, online in PDF format, helpful in getting a handle on some of the basic mathematical concepts relating to tensors: vector spaces, dual spaces, etc.

    Ray M. Bowen and C. C. Wang:
    Introduction to Vectors and Tensors, Vol 1: Linear and Multilinear Algebra

    Ray M. Bowen and C. C. Wang:
    Introduction to Vectors and Tensors, Vol 2: Vector and Tensor Analysis

    Part two of this series of video lectures from MIT has an introduction to tensors, from the second half of lecture 15 onwards, although it only deals with orthonormal coordinate systems.
    http://ocw.mit.edu/OcwWeb/Materials-Science-and-Engineering/3-60Fall-2005/CourseHome/index.htm [Broken]
    Last edited by a moderator: May 4, 2017
  6. Mar 20, 2010 #5
    Are you a Chinese?There is a series books on Differential and General Relativity written by 梁灿彬,it's nice!
  7. May 16, 2010 #6
    If you are completely lost on the math, one of my favorite intro to tensor calculus books is "A Brief on Tensor Analysis, 2nd ed." by James G. Simmonds (ISBN 0-387-94088-X). His approach is very physical, so you can let your intuition guide you until the math starts to sink in. This won't take you very far, but this is a step down to get your feet wet. It's about 100 pages long.
  8. Jun 29, 2010 #7
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