- #1

TerryW

Gold Member

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- 6

## Homework Statement

This is Exercise 19.1 in MTW - See attachment

## Homework Equations

See attachment

## The Attempt at a Solution

[/B]

I've worked through 19.3a, 19.3b and 19.3c ( see post by zn5252 back in March 2013 replied to by PeterDonis) and proved them for my my own satisfaction and I've also worked through 19.7a, 19.7b and 19.7c. My problems begin when I try to find h

_{00}and h

_{om}.

I have arrived at a solution for h

_{00}but it:

a) only works if T'

_{00}>> T'

_{ii}. (I think this is true in geometricised units) and

b) I haven't made any use of 19.7a and 19.7b and I don't see how they would be useful because the expansion of 19.2 for h

_{00}will only include terms with ##\bar{T}^{00} (= \frac 1 2 (T'^{00} +T'^{ll})##

The result of my labours for h

_{0m}is:

## h_{0m} =-\frac 1{2r}\frac{\partial}{\partial x_m} \int(T'_{00,0})r'^2d^3x' -\frac{\partial}{\partial x_m} \int(T'_{00}+T'_{ll})x^jx'^jd^3x' - \frac{x^m}{r}\frac 1{2r} \int(T'_{00,00})r'^2d^3x' ##

##\qquad \quad +\big(\frac {x^k}{r^2} \big)_{,m}\int(T'^{0j}{ }_{,0})x'^{j}x'^kd^3x'##

At this point, I can't see any way of using 19.7c to simplify my equation so I am stuck.

Any help anyone?

TerryW