Can a closed critical surface in a quark-gluon plasma serve as a model for the behavior of quantum gravity near to an event horizon?

Time stands still at a quantum critical point in the sense that correlation functions near to the critical point are approximately independent of frequency. In the case of a quantum liquid this would imply that classical hydrodynamics breaks down near to the critical point, revealing the underlying quantum degrees of freedom. An opportunity to see this effect for the first time in the laboratory may be provided by relativistic heavy ion collisions that are tuned so that the quark-gluon plasma passes through its critical point forming a closed critical surface. In this note we point out that in certain kinds of quantum fluids the temperature of a spherical critical surface will be proportional to (radius)-1 and the entropy inside the surface will be close to the Bekenstein bound. In these cases the breakdown in hydrodynamics near to the critical point might serve as a model for the behavior of quantum gravity near to an event horizon. Such a possibility is a fortiori notable because general relativity predicts that nothing should happen at an event horizon.