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I Help to understand the Retarded Function

  1. Nov 26, 2016 #1
    Hi people, help here please
    When the Einstein equation are linearized the results are the weak field Einstein equations

    $$
    \left ( -\frac{\partial^{2}}{\partial t^{2}} + \nabla^{2} \right ) \bar h^{\mu\nu}=-16\pi T^{\mu\nu}
    $$
    a solution for this equations considering the source are the Retarded function
    $$
    \bar h^{\mu\nu} (t,\vec x)=4 \int d^{3}x' \frac{[T^{\mu\nu}(t',\vec x')]_{[ret]}}{|\vec x - \vec x'|}
    $$
    with

    $$t' = t_{ret} = t-|\vec x - \vec x'|$$

    until i know "t" and "x" in spacetime are the same but what physical situation describes
    $$
    |\vec x - \vec x'|
    $$
    Is similar to electromagnestism, when $$\vec x$$ represent the place where you want calculate the potencial and $$\vec x'$$ represent the place where the charge is located?

    Thanks in advance
     
    Last edited by a moderator: Nov 26, 2016
  2. jcsd
  3. Nov 26, 2016 #2

    Orodruin

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    Your weak field equation is just a separate wave equation for every individual component. The solution is just applying the retarded Green's function of the wave equation.
     
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