Violation of Bell inequalities in an analog black hole

Signals of entanglement and nonlocality are quantitatively evaluated at zero and finite temperature in an analog 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 three-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 the entanglement of which resists partial tracing.