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Homework Help: Planck scale in extra dimensions

  1. Jan 2, 2009 #1
    Hi everybody, it's my first post on here but as i seem to have hit a brick wall with my work i'm hoping somebody might be able to help me :)

    1. The problem statement, all variables and given/known data
    I'm looking at how the planck scale is reduced in higher dimensions (ADD theories) and i've managed to reproduce an expression relating the 4-d gravitational constant [tex]G_{4}[/tex] and a fundamental gravitational constant [tex]G_{4+n}[/tex] by invoking gauss's law for gravity in extra dimensions around a line/plane of mass (due to the compactification of the extra dimensions). Here n represents the number of extra dimensions. With this i've had no problems and the answer I get seems to match the answers found in the literature.

    The issue i'm having is with relating this change of gravitational constant to a change in planck length. I've just been using the normal relation for converting G into [tex]M_{pl}[/tex] i.e [tex]M_{4+n}=\sqrt{\frac{\hbar c^5}{G_{4+n}}}[/tex] but all the papers on the subject use the relation [tex]M_{4+n}^{2+n}\approx G_{4+n}^{-1}[/tex] with this relation I get all the right answers but I can't for the life of me figure out where it comes from. Can anyone let me know where the extra factor of [tex]M_{4+n}^n[/tex] arises?

    Thanks for your time!
    Nathan
     
  2. jcsd
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