isn't it better to argue why it should have it, and then see if that proof holds?
Sure, it is. If a black hole eats mass and electrical charge, why not color charge?. But, beyond that, what should I say? I've searched google, but I didn't find anything.
Someone told me this on Tommaso Dorigo's Blog:
The classical answer is that Black holes are purely gravitational phenomena. The strong force plays no role. That's not to say that the surface of a black hole cannot be charged.
Look in any standard text book on the subject and you will find a theorem in black hole physics called the "no hair" theorem. This theorem basically says that black holes have only three externally observable characteristics, mass M , surface charge Q, and angular momentum L.
So if a Black hole can have an electromagnetic surface charge why not a chromodynamic surface charge? This is so because, as far as anyone knows, individual quarks do not exist. They exist in combinations that will have no chromodynamic color. Either a quark and antiquark, or a triad of quarks. These particles will fall into the black holes in these colorless forms, so the black hole can't gain any net chromodynamic charge.
It should also be noted that any real black hole the hole itself is likely to be neutral (Q=0) as it is constanly pulling in new particles of all kinds of EM charges.
If a BH pulls out of the vacuum a quark-antiquark pair (Hawking radiation) both the emitted quark and the BH will hadronize. Just like electron-positron collision. It should happen in the very final stage of BH evaporation.
What if there is not enough energy from the pair's center of mass to make hadronization happen? In that case, It would be expected that the BH would have a tiny color charge in relation to that other quark.
As the distance between two quarks increases the potential energy in the bond between them grows without bound until hadronization occurs.
Seen the plentiful research on Yang-Mills black hole "hair" in anti-de Sitter space (for boundary conditions)? It seems "black holes do not have color charge" only in the sense that classical relativists normally neglect everything other than gravitational and electromagnetic fields; in fact the black hole can have infinite hair by adding that many quantum fields.
In the reference frame I considered, that is, the quark's center of mass, the system feels no gravity because it is in free fall, and the kinetic energy of the quarks in relation to the center is smaller than it needs to happen hadronization.
I wasn't aware of that. Can you give me some nice references?
See for example: http://arxiv.org/abs/0708.2356
The strong force is short range compared to gravity. If it did have a color charge, you wouldn't be able to detect it, because you'd have to go within the event horizon to get anything measurable. So if you can't detect it either way, in my view, you can't proclaim that it's not there.
I did not say that! That quote is not mine!
yes you did, in post #3
No, I didn't. If you read #3, you will see that I am actualy quoting someone else from Tommaso Dorigo's blog!
Separate names with a comma.