Can EM fields exhibit the same energy-momentum tensor as gravitational waves?

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I don't know if my question belongs to this forum but I get some troubles within my approach; what would you think of a theory predicting that some EM fields can exhibit the same (type of) energy-momentum tensor (emt) than the emt associated with some gravitational waves or fields ? Such prediction, if realistic and well established would mean that it is impossible to detect a part of the gravitons, isn't it? Or is the emt not a sufficient tool to compare EM and gravitational radiations? Could this prediction explain some observations (irregularities) concerning the CMB for the low frequencies? Thanks for the help
 
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