Is there a way to see if a spin foam contains a black hole?
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: "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 vaccum 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!
This question is a bit like "Is there a way to see if a Feynman diagram contains a hydrogen atom?" In quantum field theory a typical history of the world is not a single Feynman diagram but a superposition of many Feynman diagrams. Similarly, we how that in loop quantum gravity a history of the world is not a particular spin foam but a quantum superposition of many spin foams. We do not yet know how to tell if such a superposition describes, or contains, a black hole.
This is one of the best fairly recent papers trying to understand black holes using loop quantum gravity and spin foams:
Eugenio Bianchi, Entropy of non-extremal black holes from loop quantum gravity.
It does not answer your question, but it shows what we can do at this point in time.
Thank you for your answers.
I do not think that the lack of superposition is a problem. I only would like
to exhibit a spinfoam toy model with a BH inside.
Look at this paper by Etera Livine
To get a toy Ising model, she freezes the spin to 1/2. She only keeps 4-valent graphs and so on.
Toy models have only to be pedagogical.
Maybe somebody could help me to formulate a question about LQG.
In RG we can give the point of view of different observers with a change of coordinates.
the observer follows lines parallel to his time axis.
How can we speak of the point of view of an observer who is not comoving in the spinfoam?
Thank you very much for your humble answer, Mr. Baez, and for correcting my misunderstanding. It's always a pleasure reading from you (and your puzzles!).
I think superposition is a vital aspect to any future quantum theory of gravity(it is in LQG). It might be true that it's not much discussed elsewhere but the quantum world, at least the one gouverning interactions and particles is all about superposition and histories, if not so why making new axioms and new theories?! GR is one a hell of good solver for much of what exists in cosmology or physics, you know!
In LQG, a topic on "strong singularities", which investigate the computation of some curvature invariants from geodisics. Try to see in this side.
Unfortunatly, I don't have much to help you on your next question.
Yes, according to the "Mathematical Universe Hypothesis" of Mark Tegmark, as all possible mathematial universes are equally realized. Even if this is not possible, you can easily make any statement true, for example by choosing another axiomatization of mathematics.
I read that the notion of distance cannot be given frpm the ratio volume/area. Can we say that a node is inside the BH and another one outside if there is no path in the spin network which joins them?
Spinfoams give curvatures without talking about matter. Can BH without matter exist?
First question you need to ask yourself is whether a black hole consists of two dimensional faces.
Yes areas are 2 dimentional, i suppose that something will follow...
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