Is there any experimental evidence exist that a charged particle at rest in gravitational field emit radiation and charged particle in free fall don't emit radiation ( According to equivalence principle )?
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Charged particle in a static gravitational field that is held at rest (relative to a static frame) by external forces would not be emitting any radiation. Conversely, freely moving charged particle in a gravitational field would emit radiation. So no, there are no experimental evidence for nonexisting effects. – A.V.S. Nov 23 '18 at 18:08
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see my answer here , https://physics.stackexchange.com/questions/258019/can-the-question-of-a-gravitationally-accelerated-charge-radiation-be-tested-exp/258027?noredirect=1#comment994048_258027 . imo the effect predicted mathematically cannot be measured because of the very small value of the gravitational constant, certainly no experiment. – anna v Nov 24 '18 at 11:59