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Homework Help: The Schwarzschild metric

  1. Sep 9, 2012 #1
    1. The problem statement, all variables and given/known data

    The problem is I am wanting to know if the expression on the right hand side is dimensionless.

    2. Relevant equations

    [tex]ds^2 = (1 - \frac{2GM}{c^2 r})c^2 dt^2[/tex]

    3. The attempt at a solution

    Since the Schwarzschild radius is [tex]r = \frac{2GM}{c^2}[/tex] would I be right in saying that

    [tex]\frac{2GM}{c^2 r}[/tex]

    is dimensionless?
  2. jcsd
  3. Sep 9, 2012 #2
    Yes, it is.
  4. Sep 9, 2012 #3


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    Note that it would have to be if the formula is valid since you're subtracting that quantity from 1, which is dimensionless.
  5. Sep 10, 2012 #4
    Of course it is. Note that sometime we write metric in this form:[tex]1-\frac{2GM}{r}[/tex]
    just a matter of unit conventions.
  6. Sep 11, 2012 #5
    thanks every1
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