GR weak field approx. problem with Dunsby's notes

[enomanus]

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!

 

[haushofer]

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.

 

[atyy]

You can also try p47 of Woodhouse's http://people.maths.ox.ac.uk/~nwoodh/gr/index.html . The geodesic equation of motion of the time coordinate ends up second order in the small parameter.

 

[enomanus]

Thanks! I've got the idea now!