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Imagine the void of space. It looks empty, but quantum theory tells us that space is full of "virtual particles"; pairs of positive and negative particles that come into existence, then annihilate one another. Imagine this happened right at the boundary of the event horizon of black hole. One particle would fall in, and the other would escape into space. The black hole would, in effect, lose that bit of energy. This would happen over time, and the black hole would eventually evaporate.

Hey, y’all! This is Hawking Radiation. Cool stuff! Thanks unknownconstellation!