Hawking radiation and how it causes black holes to evaporate
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I’ll start with the evaporation part. Each black hole has a “mass”, sort of like how heavy it is. If you throw an extra star (or a rock, or an unfortunate astronaut) into a black hole, the black hole gets a little heavier. But the black hole also sucks in things that don’t have any weight, such as light. It turns out that that also makes the black hole a little heavier.
If the black hole is emitting light due to Hawking radiation, then it is like the reverse of sucking in light. As a result, the black hole becomes lighter and lighter (heh!). We call this decrease in mass “black hole evaporation”. Eventually, the black hole loses all of its mass, and it simply disappears in a great final flash of light.
Now onto the origin of the Hawking radiation itself. Others have mentioned the common pop sci picture of a pair of short-lived particles popping into existence, one of them falling into the black hole and the other one emitted as Hawking radiation. I’ll take a crack at the “real” explanation that theoretical physicists actually use. It may be ELI16 at best.
First of all, the black hole doesn’t actually “emit” anything, since it is impossible for anything inside the surface of the black hole (called the event horizon) to escape its strong gravitational pull. As I’ll hopefully explain below, it is actually the black hole’s strong gravitational effect on its surrounding space that causes the empty space itself to literally glow on its own.
To explain this glow, we need to know two things—the Unruh effect and the Equivalence Principle. The Equivalence Principle says that the gravitational effect on someone standing still on the surface of, say, the Earth is equivalent to that person being constantly accelerated “upward” in empty space. In other words, to understand what you would observe right outside of a black hole, we only have to understand what you would observe if you were constantly accelerating (at a very fast rate!).
The Unruh effect is trickier. It says that even in empty space with no matter or light, an accelerating person would observe a constant light around them (albeit very faintly), simply due to their acceleration relative to the surrounding space. This light they observe surrounding them is not only real, but also looks exactly like the light naturally emitted by an object at a particular temperature, called the blackbody radiation. The faster the acceleration, the higher the “temperature” of the observed light. (I’m not aware of a simple intuitive explanation of this effect. The derivation of this effect, although short, requires knowledge of statistical mechanics, general relativity, quantum field theory, as well as the use of time as an imaginary number.)
If a person constantly accelerating in empty space should see themselves surrounded by light of a particular temperature, by the Equivalence Principle, so should a (very courageous) person standing on the surface of a black hole. (Remember, gravitational pull downward is equivalent to being accelerated upward.) This means that the person near the black hole would observe light surrounding them. This is the Hawking radiation. The stronger the gravitational pull of the black hole, the higher the temperature of the Hawking radiation.
I’m happy to go into either more details or more basics.
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