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Best introductory books on the mathematics of relativity?

  1. Nov 28, 2013 #1
    I was looking for a self-study book that is accessible by an high-school student (11th grade) for general relativity. I read reviews on "A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity" but unfortunately, it isn't available here, in India. Ready to work out the problems. It would be better if all the topics required were in one book (like the book I mentioned above).
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  3. Nov 28, 2013 #2


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    Without knowing how much math you already know, it's nigh impossible to recommend anything. You should at least know calculus of several variables (including vector calculus) and linear algebra before wandering into the mathematics of GR. That isn't to say that the mathematics of GR is hard mind you; in fact the mathematical foundations of GR are very, very easy compared to those of other physical theories such as QM and QFT. But you should know calculus of several variables and linear algebra in order to start making sense of these mathematical foundations in the first place.
  4. Nov 29, 2013 #3
    How about trying for special relativity first.

    That is far more mathematically accessible and you can start with Einstein Online. Einstein's book on special relativity math is available free...and accessible to most high school students.

    It's RELATIVITY, The Special and the General Theory, and has the math of special but not general relativity.

    The mathematics of special relativity in flat spacetime, with acceleration but without gravity, serves as an almost required introduction to that of the curved spacetime and gravity of general relativity.
  5. Nov 29, 2013 #4


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  6. Nov 30, 2013 #5


    Staff: Mentor

    Last edited by a moderator: May 6, 2017
  7. Dec 1, 2013 #6
    As an ignorant in the field, I believe this is a very wise suggestion.
    How about "Spacetime Physics", by Taylor and Wheeler?

    Also, talking about special relativity, I believe the young student should be made aware that there are basically two approaches that will produce different formulas according to what is meant by "m". In the past, introductory treatments used 'relativistic mass' and 'rest mass' (French and Rindler use this approach, for example). Nowadays it is more common to just use 'invariant mass', or simply 'mass'. Many formulae, and most notably E=mc^2, can have different meanings according to what is meant by m. Caveat emptor.

    General relativity in high school? Isn't that a bit too much?
  8. Dec 1, 2013 #7


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    I don't get why everyone is assuming that the OP doesn't already know SR. More importantly, the OP was asking about books on the mathematics of GR and not GR itself so SR is irrelevant here.

    I started learning it in high school; I don't think it's "a bit too much" in the slightest. Books like Hartle and Schutz barely assume anything with regards to the background of the reader.
  9. Dec 1, 2013 #8
    If you want to study the mathematics of GR (and perhaps not GR or SR itself), then here's a good list of books:

    Calc 3:
    Lang's Calculus on Several Variables: https://www.amazon.com/Calculus-Several-Variables-Undergraduate-Mathematics/dp/0387964053
    Spivak's calculus on manifolds: https://www.amazon.com/Calculus-On-Manifolds-Approach-Classical/dp/0805390219

    Linear algebra:
    Linear algebra done wrong: www.math.brown.edu/~treil/papers/LADW/book.pdf‎[/URL]
    Lang's Linear algebra: [URL]https://www.amazon.com/Linear-Algebra-Undergraduate-Texts-Mathematics/dp/038796412[/URL]
    or less advanced, but still good: Lang's introduction to LA: [URL]https://www.amazon.com/Introduction-Linear-Algebra-Undergraduate-Mathematics/dp/0387962050[/URL]

    [B]Elementary differential geometry:[/B]
    Pressley: [url]https://www.amazon.com/Elementary-Differential-Geometry-Undergraduate-Mathematics/dp/184882890X[/url]
    Do Carmo: [URL]https://www.amazon.com/Differential-Geometry-Curves-Surfaces-Manfredo/dp/0132125897[/URL]
    or a very nice introduction with forms by O'Neill: [URL]https://www.amazon.com/Elementary-Differential-Geometry-Revised-Edition/dp/0120887355[/URL]

    [B]Modern Differential Geometry with Manifolds:[/B]
    Lee's three books:
    [URL]https://www.amazon.com/Introduction-Topological-Manifolds-Graduate-Mathematics/dp/1461427908/[/URL] (this is more an introduction to topology, but this is still part of the math of relatvity)
    [URL]https://www.amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/dp/1441999817[/URL] (The very best intro book on smooth manifolds and differential topology)
    [url]https://www.amazon.com/Semi-Riemannian-Geometry-Applications-Relativity-Mathematics/dp/0125267401[/url] (must read if you're into relativity, but it's best to do the previous books first)
    Last edited by a moderator: May 6, 2017
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