Bipartite and tripartite entanglement in a Bose-Einstein acoustic black hole

We investigate quantum entanglement in an analogue black hole realized in the flow of a Bose-Einstein condensate. We argue that the system is described by a three-mode Gaussian state and construct the associated covariance matrix at zero and finite temperature. We study the associated bipartite and tripartite entanglement measures and determine the best experimental configuration for their observation.