As far as I understand the popular science explanation of black hole evaporation, quantum fluctuations of vacuum at the event horizon create a pair of matter-antimatter particles. One escapes thus reducing the mass of the black hole. So far so good. However, just outside the horizon, the same effect must be continually feeding new particles into the black hole. The outside sphere is somewhat bigger, there must be more mass entering than leaving.One thing to keep in mind is that the formation of virtual particles just outside the event horizon comes from "borrowed" energy. Under normal circumstances, these particles only exist briefly, before rejoining and returning this borrowed energy. It is a quirk of QM that allow this to happen without violating energy conservation.
I suspect he popular explanation must be leaving out some important details?
If, however, one of the particles crosses inside the event horizon before the rejoining can occur ( it does not matter whether it is the particle or anti-particle), You are left with a lone particle. The energy books must be balanced in order for this particle to continue to exist, and this come from the mass of the BH. One of the virtual particle pair has become a real particle at the expense of the BH. This particle may escape, or more likely interact with another particle which produces light radiation that does escape the region near the event horizon. You end up with some "leakage" of radiation.
That being said, only black holes below a certain size would end up experiencing net shrinkage through Hawking radiation. One of the features of Hawking radiation is that it increases as the mass of the Black hole decreases. Large black holes lose mass through Hawking radiation at a much lesser rate than they gain it from other sources. Any stellar sized black hole, even if far away from any matter that it could absorb would still be gaining mass from just the cosmic background radiation faster than it lost it through Hawking radiation.
For a black hole to lose mass faster than it gains it from the CMBR, it could not be any more massive than our Moon.
This is much smaller than any black holes that form today, but there is some speculation that small or "quantum" black holes could have formed during the early universe. It is possible that some of them survived to our time.
Even present day large black holes are subject to eventual evaporation. As the universe continues to expand, it cools which decreases the intensity of the background radiation. At some point it will cool enough for stellar mass black holes to begin to evaporate as they lose mass faster than they gain it even through the CMBR. But we are talking about really, really, really long time scales.
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