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Main/Non Absorbable constant

  1. Oct 16, 2012 #1
    Well I have the metric of a sphere given as:
    ds2= α (dθ2+ sin2θ dφ2 )

    And I'm asked to prove that the constant α is non-absorbable by proving there is no solution to this set of equations:
    Δξgμν = ∂gμν/∂α

    where:
    Δξgμν = gμν;λ ξλ + gλν ξλ + gμλ ξλ


    Finally, I'm asked to provide a second way to prove that α is non-absorbable.



    I don't understand what it means by non-absorbable at all. Do you know where am I supposed to find what it is? From books I have Weinberg's "Gravitation and Cosmology Principles and appls of GTR". In addition, any hint would be appreciated...
    Thank you..
     
  2. jcsd
  3. Oct 17, 2012 #2
    28c3d3m.jpg

    This is my 1st try to solve it, the equations I ended up are the 5 bellow, which cannot be solved (i guess). The last one reads ξ2,2=1/2α..

    I also got a problem with 0=1...

    What do you think?
     
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