  Signals of entanglement and nonlocality are quantitatively evaluated at zero
and finite temperature in an analogue black hole realized in the flow of a
quasi one-dimensional Bose-Einstein condensate. The violation of Lorentz
invariance inherent to this analog system opens the prospect to observe 3-mode
quantum correlations and we study the corresponding violation of bipartite and
tripartite Bell inequalities. It is shown that the long wavelength modes of the
system are maximally entangled, in the sense that they realize a superposition
of continuous variable versions of Greenberger-Horne-Zeilinger states whose
entanglement resists partial tracing.
