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Has anyone ever tried to derive gravitoelectromagnetic waves equation? As we know, there is Maxwell-like equation in gravity. Has anyone here ever formulated gravito electromagnetic waves equation using Maxwell-like equation in the same way with electromagnetism? If so, I want to know the properties of that waves based on the equations. Is it same with gravitational waves?

I am actually working on this, but I still don't know the physical meaning of that waves.

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    $\begingroup$ Your link includes GEM's version of Maxwell's equations, from which you can obtain wave equations. However, the way $\rho,\,\mathbf{J}$ transform from one reference frame to the next is non-Lorentzian, as noted near the end. $\endgroup$
    – J.G.
    Commented May 9, 2018 at 14:34

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