Dear Naima,
This is a good question. I hope you will be briefed on the matter soon. But I wouldn't call my argument an answer so I'm sorry.
In the words of
John Baez[1]: "
A spin foam is a 2-dimensional cell complex with faces labeled by representations and edges labeled by intertwining operators; generically, any slice of a spin foam gives a spin network. It's applied to operators representing space-time. Like using feynmann "trees" in LQG, in a sense.
Besides, a black hole is a region of space-time, where no longer the others forces, except of gravity, play a role. So we don't talk about protons, muons, strong force or quarks. What lies "inside it" is certainly-but not yet confirmed-quantized for sure. The "real " content of a black hole is at most "informations", coded on the event horizon(null hypersurface), if I may say. So the nodes, or vertex and edges,..everything is on this surface.
You don't need to mix between the two concepts. Yes, the vertex notion in spin foams sounds like a singularity, yet it's just a topological notion, used mainly in the diagrams and calculations of index and histories. The black hole's singularity-the infinite point- can't exist "on" the said surface, it's "behind and covered within or hidden" just like the censorship hypothesis requires it! A future true gravity theory must explain black holes on a complete new ground, without infinite gravity or infinitely curved space, without the need for singularities (like was the case with QED and vacuum polarization).
I fear that, at this point, my talk has became mainly personal ideas and is nowhere true until reviewed by others..
Thanks and good luck!
Samir.
[1]:
http://math.ucr.edu/home/baez/foam/