DaveC426913 said:
How can gravitons escape a black hole? Presumably they must, in order to have an external gravitational effect.
No, they don't have to. The gravitational effects observed at any event in a spacetime are entirely due to what is present in the past light cone of that event. For any event outside the horizon, no event on or inside the horizon is in the past light cone, so no such event is relevant for determining the gravitational effects observed.
DaveC426913 said:
I'm sure this is a naive GR-based model of a BH.
No, a GR-based model has the property I just described. When you think in terms of "gravitons having to get out of the BH", you're thinking in terms of a naive QFT-based model of a BH--but even such a model will still have the property I described above, so there is actually no need to consider how gravity "gets out" of the BH in that model either. See below.
DaveC426913 said:
I guess a BH is a different animal in the QM world?
We actually don't know what kind of animal a BH is in the QM world, since we do not have a good theory of quantum gravity.
However, we do know that there is a well-defined quantum field theory of a massless spin-2 field, whose classical limit is General Relativity. This theory works similarly to quantum electrodynamics, which is the QFT of a massless spin-1 field. In both theories, you can, at least in perturbation theory, model the interaction (gravity or electromagnetism) as the exchange of virtual gauge bosons (gravitons or photons), and virtual particles have nonzero amplitudes to be exchanged between spacelike separated events, so they are not confined to light cones, and therefore
virtual gravitons could, in principle, get out of a BH to mediate a gravitational interaction between the hole and something outside.
Note, however, that this viewpoint is heuristic and limited, for three reasons: (1) because it is based on perturbation theory, and it is not at all clear that perturbation theory is sufficient to model a BH; (2) because the QFT of the massless spin-2 field that I just described is not believed to be a viable fundamental theory of quantum gravity anyway, for various reasons that the margin of this post is too small to contain; and (3) because, as I said above, QFT still has the property I described at the start of this post, which means we don't actually
need to invoke stuff like virtual gravitons escaping from a BH to explain the gravitational effects observed outside one.
See this article by John Baez for a similar answer to the above:
https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html