Does everything (all matter) emit radiation? What about if something is at absolute zero? What about if it’s inside a black hole? Does a black hole emit radiation? Are Hawking particles emitted by the black hole or are they spontaneously created? If a black hole causes particles to be created, is that the same as the black hole emitting them?
To begin with, matter always emits radiation. That’s because, at any temperature above absolute zero, the electrically charge particles in matter are in thermal motion and they accelerate frequently. Any time an electrically charged particle accelerates, it emits electromagnetic radiation. If you could cool matter to absolute zero, the thermal motion would vanish and the matter wouldn’t emit radiation. However, absolute zero is an unreachable destination—it can’t be achieved—so everything experiences thermal motion and emits radiation.
The issue of radiation emitted by a black hole is another story. For decades, people thought of a black hole as perfectly black—it absorbed radiation perfectly but emitted none itself. However, Stephen Hawking showed that a black hole does emit radiation and that it behaves like a normal blackbody: an object that emits thermal radiation characteristic of its temperature. The temperature of a black hole is inversely proportional to its mass. For black holes of any reasonable size, this temperature is so extraordinarily low that the black hole emits very little Hawking radiation.
This radiation originates in the vicinity of the event horizon, the surface inside which the black hole’s gravity finally becomes strong enough to prevent even light from escaping. At that surface, quantum fluctuations in which particles are temporarily created and destroyed can occasionally lead to the creation of a particle that escapes the black hole forever. In effect, two particles are created simultaneously, one of which falls into the black hole and is lost and the other of which escapes forever. The particle that falls into the black hole actually decreases the mass of the black hole, and the missing mass escapes with the other particle. As for whether the black hole causes this emission or is actually doing the emission, there is no difference. The only feature that the black hole has (other than electric charge and angular momentum) is its event horizon (actually a characteristic of its mass). If the event horizon is causing the particles to be created, then the black hole itself is at work creating those particles.