How can a black hole "evaporate"?

According to theory, a black hole can still support it's outer
gravitational field, even though its escape velocity is faster than
light (and light-speed gravitons), on relic gravitation.

According to General Relativity, from an outside reference frame, a
black hole takes forever to form. So there will never be a time when
light-speed gravitons, forming the gravitational field, get trapped
inside the black hole.

But from the perspective of the black hole forming, or someone falling
into a black hole, everything takes place in a short amount of time,
and the outside universe rushes through an infinite amount of time in
a heartbeat.

So if virtual particles were to be split up by one of the pair falling
into the black hole and the other radiating away the mass of the black
hole, wouldn't that have to happen an infinite time in future after
the black hole forms?

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David A. Smith