A charged black hole is accelerated by the gravitational field due to some other body. Does this gives rise to radiation from the charged BH? If so do the photons from this process escape? Is this related to Hawking/Unruh radiation?

Yeah, and it must be. I am not an expert on the subject, but from what I can guess, the passing gravitational waves will cause the energy around the black hole to fluctuate, and they will polarize the space on either side due to the energy difference. The result would effectively polarize the vacuum, and particles (and their anti-partners) are created around the surface of the black hole. Of course, Hawking radiation will occur when one particle fails to annihilate and falls into the black hole, causing the other particle to become real and thus the black hole loses energy in the form of radiation.

I am guessing on a fair bit of that, but it makes sense to me.

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