Weak Field approximation -- quick sign question

  • Thread starter binbagsss
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  • #1
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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..
 
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Answers and Replies

  • #2
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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.
 
  • #3
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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.

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?
 
  • #4
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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?
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.
 
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  • #5
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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.

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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