Hawking radiation and how it causes black holes to evaporate
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The radiation part has been adequately explained (or at least a simplification has). Now, for the evaporation bit:
You may know E=m c^2. This equation means that energy and mass are kinda the same. Now, energy is conserved in any closed system. This means that, if a black hole is sometimes radiating out particles with mass, and thus energy, the black hole must be losing that mass/ energy. So, as long as the black hole is not sucking up more energy than it is losing, it will shrink. Currently most black holes are probably not shrinking, since they have many chances to gobble up massive things, and because even empty space has some energy to be eaten- the cosmic microwave background radiation means space is not absolutely cold, but is at about 3K, so there is an energy source for even the loneliest black holes- for now! Space is getting colder, and stuff is getting further apart, so one day the background heat won‘t be enough, and black holes won‘t find any big things to gobble up.
Now, Hawking radiation is a property of the surface of the black hole*. More surface means more hawking radiation. Since small 3D objects have more surface by comparison to their volume (a 100 by 100 by 100 cube has volume 1 million, but surface 60 thousand, while a 1 by 1 by 1 cube has volume 1 and surface 6), smaller black holes actually give of their energy faster in proportion to the energy the hole has stored. This means that this creates a runaway effect, and the black hole shrinks faster and faster**. Now, this doesn‘t mean the process is fast by any means- solar mass black holes probably take ~10^67 years to evaporate.
*Here I mean the surface of the sphere with radius equal to the schwarzschild-radius. The black hole itself maybe kinda possibly doesn‘t have a defined area.
**It can be shown that the emitted power is proportional to mass^-2. So, halve the mass, four times the radiation.
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