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Homework Help: Gravitational waves

  1. Apr 19, 2007 #1


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    1. The problem statement, all variables and given/known data
    I am given the form of the perturbation in the metric:

    [tex]h_{\mu\nu}=\left(\begin{array} {cccc} 0&0&0&0 \\ 0&1&0&0\\ 0&0&-1&0 \\ 0&0&0&0\end{array}\right) \gamma e^{-(z-t)^2}[/tex]

    Where gamma<<1. That is to say, [tex]g_{\mu\nu}(\mathbf{r},t)=\eta_{\mu\nu}+h_{\mu\nu}(\mathbf{r},t)[/tex] (we use (+---) for eta (Minkowski))

    h (or rather, all 16 of its terms) has the form of a plane wave sailing in the z direction at the speed of light c=1.

    I am simply asked to find the gravitational energy transported by (transerse) unit area by the wave from t=-infty to t=+infty.

    3. The attempt at a solution
    I was about to write h as a fourier integral but I don't know what I'm gonna do after that, so is this even a good start?
    Last edited: Apr 19, 2007
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