Understand intuitively 4th boundary condition of gravitational wave

Suppose we have a gravitational wave which obeys the equation:

$[G_{tt}-c^{2}G_{xx}]h_{\mu\nu}=0$

Lets take the case where $h_{\mu\nu}\ne0$ so we are left with the classical wave equation.Suppose for simplicity that the gravitational wave has a wavelength of 1m so we get the following boundary condition:

$G(0,t) = G(1,t)$

Lets assume that at x=0 there is the source of the gravitational wave so lets make

$G(x,0)=\delta(x)$

Now I have to pick a 4th boundary condition($G_{t}(x,0)$)but what does the $G_{t}$ mean physically for the gravitational wave??

posted 11 months ago

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Volpina‭

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