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GR weak field approx. problem with Dunsby's notes

  1. Sep 7, 2009 #1
    Hi again,
    Thaks for previous help. I am self studying GR using Schutz and Dunsby's webpages & notes.
    I am stuck on a step in the derivation of the weak field approximation.
    They approximate the metric with g[a][/b]=n[a]+epsilon h[a]
    In step 7.30 the partial derivative h[0],[0]is taken as zero to get (7.30), -1/2 epsilon h00,i
    He has neglected the time derivative!
    Can you explain Why??
    Thanks for any help!!!
     
  2. jcsd
  3. Sep 7, 2009 #2

    haushofer

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    Hi enomanus,

    the Newtonian limit consists of the following:

    -Take the velocity of the testparticle much smaller than c.
    -The gravitational field is weak, so we can make an expansion around the vacuum (in your case minkowski space time).
    -The field is static.

    This last assumption should be mentioned somewhere in your notes, otherwise you could check the notes of Sean Carroll,

    http://arxiv.org/PS_cache/gr-qc/pdf/9712/9712019v1.pdf

    chapter 4 page 105.
     
  4. Sep 7, 2009 #3

    atyy

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    Science Advisor

    You can also try p47 of Woodhouse's http://people.maths.ox.ac.uk/~nwoodh/gr/index.html [Broken] . The geodesic equation of motion of the time coordinate ends up second order in the small parameter.
     
    Last edited by a moderator: May 4, 2017
  5. Sep 13, 2009 #4
    Thanks! I've got the idea now!
     
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