The uncertainty principle implies that even empty space is filled with pairs of particles and anti-particles. These appear together at some point of space and time, move apart, and then come back together, and annihilate each other. If a black hole is present, one member of the pair may fall into the black hole, leaving the other without a partner with which to annihilate. The forsaken particle or anti-particle, may fall into the hole as well, but it may also escape from the neighbourhood of the black hole. To someone at a great distance, it would appear that the escaping particle had come from inside the hole.
