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FLRW metric (please help)

  1. Dec 18, 2008 #1
    Hi all,

    I have found the "generic" form of the FLRW metric:
    [tex]ds^2=(cdt)^2-dl^2[/tex]

    And I have found the three-dimension spatial metric for euclidian space (K=0, spherical space K=1 and hyperboloid space (K=-1):

    [tex]dl^2=a^2(dr^2+r^2d\Omega^2)[/tex]

    [tex]dl^2=a^2(\frac{dr^2}{1-r^2})+r^2d\Omega^2)[/tex]

    [tex]dl^2=a^2(\frac{dr^2}{1+r^2})+r^2d\Omega^2)[/tex]

    BUT how do I find the "general" form of the FLRW metric, how can I include the curvature parameter K?

    Please help, I really need it!

    Best regards.
     
  2. jcsd
  3. Dec 18, 2008 #2

    marcus

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    What happens if you just stick a K into the formula, with the understanding that it can take on just those 3 values: -1,0,and 1? Don't you get the three cases you want?

    [tex]dl^2=a^2(\frac{dr^2}{1-Kr^2})+r^2d\Omega^2)[/tex]

     
  4. Dec 18, 2008 #3
    Thank you very much for you answer, I really appreciate it!

    Yes, you are right I get the cases I want. But are you questioning to be ironical or are you sure it the correct way? :)

    Love this forum, I'm gonna contribute

    Best regards
     
  5. Dec 19, 2008 #4

    cristo

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    It is the correct way. The general form for the line element is the one that marcus gives. Plugging in values for k gives you the three specific line elements.
     
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