Ah hawking radiation. Where classical and quantum physics meet in the weirdness of black holes to form some unholy offspring.
So space is a vacuum. We say that theres nothing in it. However, there’s something called the Heisenberg uncertainty principal which I call the “nothing is true, everything is permitted” rule from quantum physics. This states that the vacuum isn’t truly empty, instead it has an anti particle and a particle which spontaneously appear and then destroy each other over an absurdly short amount of time.
That is true everywhere but in normal regions of space this makes absolutely no difference. A black hole is pretty extremely far from a normal region of space though. What happens there is the particle and anti particle are created near the event horizon but one falls over the horizon into the black hole. This leaves the other to escape and become a real particle radiating away from the black hole – Hawking radiation.
TLDR: quantum physics is weird and vacuums aren’t empty.
Both the other commenters explain Hawking Radiation as virtual particles falling into the event horizon, which is weird because that’s not actually what’s going on. What happens is that the existence of the event horizon cuts off certain vibrational nodes in the quantum fields of some particles, which allows energy to leak out of the black hole. Think of a quantum field as an infintely large drumskin, and think of particles as specifc arrangements of waves traveling across the membrane. A black hole is roughly analogous to cutting a hole in the membrane, and Hawking showed that doing so changes the resonant properties of the entire drumskin. We observe that the field around the black hole must be “excited” to a specific energy level, and that energy comes from the black hole. This looks an awful lot like heat emission, and we see that excited quantum field as the spontaneous generation of particles that we call Hawking Radiation.
Hawking radiation is what happens when general relativity (gravity) and quantum mechanics (really small things) run headlong into each other. It’s a way for a black hole to emit radiation even though our conventional understanding is that nothing can come out of the black hole. And, strictly speaking, it’s not, but that’s where quantum weirdness comes in.
Quantum mechanics suggests, among other things, that at very small scales (very short distances, very short times) pairs of particles and anti-particles can arbitrarily pop in and out of existence. This happens so close together and for such short periods of time that, at our macroscale, we never notice. But if it happens that if the pair pops into being right on top of the event horizon of a black hole (which isn’t a physical thing, just a mathmatically defined boundary in space), one half of the pair can be inside the event horizon and one half can be outside.
The one on the inside gets sucked in. The one on the *outside* has no opposite member to mutually annihilate with and promptly goes zipping off at lightspeed…tah dah, radiation.
From an energy and mass balance point of view it makes it look like the black is emitting radiation and “evaporating” (losing mass). Nothing is actually escaping the hole though. The way the math works out, this happens much faster with very small black holes and suggests that tiny black holes, if they exist, have very short lives.