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I am reading Feynman's lectures on gravitation.

The equivalence principle says that no local measurement (it includes measurement of the electromagnetic field) can tell you if you are accelerated or in gravity.

Feynman agrees and writes that we have then a problem. Accelerated charges are the sources of radiations but what about motionless charges in gravity emitting photons?

He writes that Maxwell's equation will have to be rewritten to be coherent with this principle.

I have two questions.

Is there a mainsream theory for these new equations?

Did experiments show that motionless charges can emit in gravity?