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There won't be any radiation from a supermassive black hole, or a stellar mass black hole. The bigger a black hole is, the colder it is, and any black hole bigger than a thimble is colder than the Cosmic Microwave Background. Its brightness isn't technically zero, but it's still darker than the background, and it's absorbing heat (and getting slightly bigger) rather than giving it off.

Whether or not it is absorbing radiation faster than it is emitting is not relevant to whether or not it is emitting at all. Black holes are pretty dang black but they are not "0 by definition".

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