I understand (I may be wrong) that the highest density material is that of a quark-gluon plasma, such as the interior of a neutron star. Is there an upper limit to this density and is it known?
According to our current understanding a black hole will form at some point if you keep increasing the density. The density where this happens would then be the upper limit for the density (and we are far from any such limit at today's colliders). Strongly interacting matter at these high densities is a question of current research. Some keywords to look for are "quark star", "quark matter", "color superconductivity", "color-flavor locking" and "QCD phase diagram".
Not sure that it answers your question but there's some interesting stuff in this paper- Strange Quark Matter and Compact Stars http://arxiv.org/abs/astro-ph/0407155
There was a hidden question related to my original question. You have opened it up. What I was driving at is the conflict between General Relativity and "physics", i.e. quantum theory. General relativity predicts that inside a black hole everything gets condensed to a point of infinite density. If there is an upper limit to the density of matter, then there would be a contradiction.
According to the paper in post 4, on page 62, a max density for quark stars appears to be 1500 MeV/fm^{3} and if my calculations are correct, this converts to about 2.674x10^{15} g/cm^{3}. In this paper on page 4, the max appears to be approx 3.2x10^{15} g/cm^{3}. According to another source- 'The maximum density of stable objects in hydrostatic equilibrium is 10^{16} g/cm^{3}. This limit applies to any macroscopic object composed of standard model fermions' which works out at 10 billion tonnes per cm^{3}. Hypothetical Preon degenerate matter is suppose to occur at densities around 10^{20} g/cm^{3}. Though I always thought that once inside the Schwarzschild radius, the world lines became space-like and there is no stable radius so no matter how much pressure the degenerate matter might exert, r is temporal and will not 'hold' and it's this that predicts the singularity (though in the case of the rotating black hole, time-like world lines are reinstated beyond the Cauchy horizon and matter may still exist in some form).
Well, there could be some modification of GR where quantum mechanics becomes relevant. A high density without a black hole is possible if the object is small enough.
This is sort of what I was getting at. G.R. will predict that all matter ends up as a singularity, but Quantum theory gives an upper limit to density. Put this together and you see a need for a newer theory.
Well, that's not really news is it? We have known for a long time that we can't describe phenomena where a quantized theory of gravity is needed. Hence the big interest in creating such a theory. In any case, quantum gravity does not have much to do with the quark-gluon plasma, so regardless of what the density is in the quark-gluon plasma it has small, if any, impact on quantum gravity research.
The current belief is that neutron stars do not contain quark-gluon plasmas. A neutron star interior is much colder than the quark-gluon plasmas created at CERN. I don't see why there should be an upper limit on density of small objects, though such density might be very transitory.
http://en.wikipedia.org/wiki/Neutron_star Above description describes the structure of a neutron star. It says that the deep interior may be a quark-gluon plasma.
There is no contradiction. The limit is for the density of stable matter in hydrostatic equilibrium. These conditions do not apply to interior of a black hole.
That's not right.Both GR and QM seem to work fine both inside and outside of the B-hole, except near the singularity at the center.
No doubt. But the point here is that the mere fact that there is probably a maximum density for stable matter isn't in itself necessarily cause for concern because it doesn't show any inconsistency. The limit is probably true but only applies to matter under hydrostatic equilibrium. This condition doesn't apply to a Black hole so there is no obvious contradiction.