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Following Landau&Lifschitz (L&L) (I´m not a researcher in GTR) it is possible to arrive to a 3D version of Maxwell equations in a GTR-correct form. These equations resembling the ones in a dispersive electric and magnetic material, suggest, at first glance, that there should be a dispersion relation for EM waves propagating in a gravitational field. In fact, after a naïve algebra-struggling, it is possible to get to equations with a dispersion-like form.

However, if this was true, the radiation of an explosive event would arrive at different times for different wavelenghts, in a classical GTR formulation which is not correct (as far as I know) since then there should be local effects that could tell an observer about absolute positions and velocities with respect to the source.

I know there is some Loop Quantum Gravity results that suggest it is possible, but in Quantum Gravity scenarios, to have this effect.

The point is that I cannot find the L&L-inspired formulation wrong, nor can I accept it.

Can somebody shed some light on this ignorant-fellow?