Guest Dave,
This was Hawking's first great achievement, his second being pair production near the event horizon, and eventual evaporation of black holes.

I was ware of that second achievement, and he laid it out again very clearly in his Reith lectures in recent weeks.

There is something I have not understood that I think you will be able to explain. One of each pair goes off to infinity as Hawking radiation, and the other falls into the hole.
How does that result in a loss of mass from the black hole?