Based on external observations of black hole "event horizons" (the areas surrounding black holes inside of which everything falls in) it appears that black holes may spin very rapidly. (Not all black holes have to spin, but the ones we have so far located do -- we locate them by the results of the spin.) By a process called "frame dragging" everything around a spinning hole also spins with the hole. Lots of synchrotron radiation and magnetism is generated as particles at and just outside an event horizon approach the speed of light. High-energy gamma rays become common and they can result in one of several kinds of matter/antimatter particle pairs that appear to come into temporary existence spontaneously. This kind of thing happens all the time all over the universe, and normally the particle and antiparticle annihilate each other within billionths of a second and preserve the parity required by quantum theory. But, if it such a pair pops into existence right at a black hole event horizon, there are three possibilities: depending on the direction of the forces in original energy, both the particle and anti-particle can fall in (and then quickly annihilate); or they can both escape (and then quickly annihilate); or one can escape and the other fall in (before they have a chance to annihilate.) This last possibility leads to the conjecture about "evaporation" of the black hole and to theoretical "Hawking Radiation".
It doesn't matter which of the matter/antimatter particle pair falls in, as long as the other does not. The in-falling particle or antiparticle forces the black hole to cough up an opposite from inside the event horizon, and the two annihilate. And that leaves a deficit: there is now either a particle or an antiparticle somewhere in the black hole without a partner. The partnerless particle or antiparticle can't escape, and the mass of the black hole decreases by the amount of the mass of the annihilated particle or antiparticle. Eventually the extra particles and antiparticles inside the hole find each other and also annihilate, but those annihilating pairs do not account for the missing particles and antiparticles. When this scenario plays out often enough, the mass of the black hole decreases to the point that the hole no longer has enough mass to suck everything in, and it is no longer a "black hole" -- it has "evaporated".
The escaping halves of pairs separated at the event horizon are called Hawking Radiation, but nobody has detected it yet, because the flow of everything else into the kind of black holes we currently can find dwarfs the tiny amount of theoretical Hawking Radiation outflow. That being the case, why should we believe that any of the above theory really happens? The answer is all those missing smaller black holes. They don't seem to be there, so they must have evaporated.
Black hole evaporation:
Stephen Hawking's Internet site:
PS -- Evaporation has been going on since the beginning, about 16 billion years according to the latest estimates. Hawking's theory about evaporation is 25 years old. Only now are we approaching the instrumentation that allows us to find black holes so we can hope to start checking out the theory.