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Precession of the perihelion - Schwarzschild metric

  1. Nov 4, 2006 #1


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    Hi everyone!!!
    I was trying to solve this question following the Hartle's book (Gravity: an introduction to Einstein’s general relativity) , exercise 9.15, but I don't know how to do the expansion of (1-2GM/c^2r) in powers of 1/c^2...

    I know this sounds easy, but I couldn't get the expression from item (b)

    Can someone please help me to expand to get the right answer
  2. jcsd
  3. Nov 4, 2006 #2


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    For those who don't have the book, what I want is to get this equation:

    from this one:

    My problem is how to get the first term (in front of the first integral), only by expanding the (1-2GM/rc^2) in powers of 1/c^2. Someone?
  4. Nov 4, 2006 #3


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    Staff Emeritus
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    What you need to do is to get the expression in the form


    where u << 1

    This can be expanded by the binomial theorem as

    1 + n u + n(n-1) u^2 + ...

    It looks like you will have to do this twice. The first step would be to consider the case where n=-1 and u = 2GM/c^2 r. Then you have to apply the same idea again with n=-1/2 and a much more complicated expression for u.
  5. Nov 5, 2006 #4


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    Thank you!!!
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