[Friend of thunder]

It's called "Hawking Radiation" and it's why Stephen Hawking became a big deal. He figured out it had to exist, computationally, based on quantum mechanics.

I read his book A Brief History of Time but could never understand that; to me it implies the material must be traveling faster than the speed of light. Hawking explains it, in part by saying

So in empty space the field cannot be fixed at exactly zero, because then it would have both a precipice value (zero) and a precise rate of change (also zero). There must be a certain minimum amount of uncertainty, or quantum function, in the value of the fields.

A Brief History of Time Page105

The math to understand Heisenburg – who is clearly implied in this statement – is way beyond me (that is why I am a production manager and not a cosmologist). If you could explain how material leaves a black hole (to me that implies crossing the event horizon in the wrong direction –I realize I am not thinking ‘quantumly’) without travailing faster than light, and do it with out higher mathematics, I would be very interested.

[ExpandNATO]

The simplest explanation of Hawking radiation is simply that the border of the black hole is not fixed at the quantum level, but is constantly wiggling/vibrating. A particle can suddenly find itself outside the black hole, not because it somehow escaped, but rather because the border moved.

Second attempt, in the quantum world particles can and do go from one state to another without going through what is in between (quantum effect in a tunneling diode). If there is a non-zero quantum function at a point in space, then a particle can appear there (and as Hawking notes empty space cannot have a field fixed at zero).

The source for the first paragraph was a popular science magazine and for the second my memory of long ago physics and electronics courses, so both may be completely wrong or greatly oversimplified.