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Ricci tensor in FRW metrics

  1. Jan 26, 2013 #1
    Hi does anyone know a formal definition for why off diagonal ricci tensors are equal to zero in a symmetric standard FRW metric?
     
  2. jcsd
  3. Jan 26, 2013 #2

    bcrowell

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    Is this in a particular set of coordinates?
     
  4. Jan 26, 2013 #3
    yeah sorry (t,r,\theta,\phi)
     
  5. Jan 26, 2013 #4

    bcrowell

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    I think it follows from symmetry. For instance, [itex]R_{\theta t}[/itex] flips signs under a change of coordinates [itex]\theta\rightarrow \pi-\theta[/itex], so if it was nonzero it would violate isotropy. Under the same transformation [itex]R_{\theta\theta}[/itex] stays the same.
     
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