Undergrad Help Understand Retarded Function: Einstein Eq. Linearized

[needved]

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

 

[Orodruin]

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.