Think of some stuff falling together to make a black hole. Even when the stuff is sitting around as some sort of star, it has a gravitational field. As it starts to collapse, it doesn't have to send out a new field- the old one is already out there.
i know this is only a partial answer, but maybe it's a useful start.
Here’s another partial answer: The gravitons are not "on shell" -- that is, they do not have the relationship between energy and momentum given by special relativity because they are virtual particles, exchanged as intermediate quantum states. For the same reason, the photons exchanged in the electrostatic force between two stationary charges are virtual particles.
A charged black hole will still have its electric field around it (otherwise you violate Maxwell’s equations and the conservation of electric charge) after it collapses. The electric and magnetic interactions are mediated by virtual photons. I guess that the same sort of argument that lets black holes have electric and magnetic fields also allows gravitons to propagate.
One feature of this -- the space and time inside the event horizon is causally disconnected from the rest of the universe. That is, any event that happens inside the event horizon is incapable of affecting events outside. So there can be no transmission of information outside of the event horizon. The static electric and gravitational fields however do not carry such information, and bursts, burps and upsets happen only as stuff falls in and radiates real photons and gravitons as it does so.
Correct me if I’m wrong! (but I know the answer is incomplete).
(published on 10/22/2007)