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Scalar curvature

  1. Jul 27, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the equation of scalar curvature for homogenous and isotropic space with FLRV metric.

    2. Relevant equations

    ## R=6(\frac{\ddot{a}}{a}+\left( \frac{\dot{a}}{a}\right )^2+\frac{k}{a^2}) ##


    3. The attempt at a solution
    ##G_{AB}=R_{AB}-\frac{1}{2}Rg_{AB}##
     
  2. jcsd
  3. Jul 27, 2013 #2

    WannabeNewton

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    That's not really much of an attempt to be honest :p

    What did you get when you calculated the Ricci curvature for the FLRW metric? Just plug the metric into the formulas.
     
  4. Jul 29, 2013 #3
    If I strart from this point:
    ## B_{\mu\nu}+\lambda g_{\mu\nu}B=0 / \cdot g^{\mu\nu} \\
    R(1+4\lambda)=0 ##
    what next?
     
  5. Jul 29, 2013 #4
    Any help?
     
  6. Jul 29, 2013 #5

    WannabeNewton

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    I can't really understand your notation. Why not just calculate it directly? ##R = g^{\mu\nu}R_{\mu\nu} = g^{\mu\nu}R^{\alpha}{}{}_{\mu\alpha\nu}##. The FLRW metric is diagonal and extremely simply in the usual form so the computation shouldn't be so bad.
     
  7. Jul 30, 2013 #6
    With the FLRW metric actually you should be able to use directly the definition of ##R_{\mu\nu}## and then take out the scalar as here above.
    Anyway try and look in any GR book (e.g. Carroll or others). It is done quite everywhere.
     
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