If EM waves create gravitational field "around" them (as I understand is the case) which reference frame we should use? We could imagine several observers, some moving in the same direction with EM wave with different speeds, others moving in the opposite direction. The different observers could measure very different energy levels for the EM wave, so maybe we could expect very different gravity fields depending on the observer. Are all fields equally correct or should we pick one? Sorry if this is old question, but I didn't find anything exactly matching. Thanks.