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Weak Field approximation -- quick sign question

  1. Mar 27, 2015 #1
    http://www.mth.uct.ac.za/omei/gr/chap7/node3.html [Broken]

    Shouldn't eq 45 have a minus sign, looking at eq 29.
    Although I'm confused because the positive sign makes sense when comparing with the Newton-Poisson equation.
    I can't see a sign error in eq 29.

    (I believe the metric signature here is (-,+,+,+))

    Anyone?
    thanks..
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Mar 27, 2015 #2

    Mentz114

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    When you lower the derivative index of ##{h_{00}}^{,i}## in (29) it changes the sign. I think what is written on that page is correct.
     
  4. Mar 27, 2015 #3
    Ahh thanks,
    but these are not covariant/contravariant derivatives they are just partials , is this correct?

    Also if equation (29) has an upper index then I thought (45) would have one upper and lower?
     
  5. Mar 27, 2015 #4

    Mentz114

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    Yes, the comma usually means partials, the semi-colon is used for covariant derivatives.

    We have (29)

    ##{\Gamma^i}_{00} \approx -\frac{1}{2}\epsilon {h_{00}}^{,i}##

    which has one upper index only because ##h_{00}## is a number ( a component).

    In (45) ##{\Gamma^i}_{00,i}## has no indexes because ##i## is summed over. This is a scalar which it must be to give us Poisson's equation.
     
    Last edited: Mar 27, 2015
  6. Mar 29, 2015 #5
    I mean the ##h_{00,ii}## in [45], Taking a lower derivative of (29)-##{\Gamma^i}_{00,i}## I thought would give ##h_{00,i}^{,i}##
     
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