The entropy of an acoustic black hole in Bose-Einstein condensates

Abstract

We compute the entanglement entropy associated to the Hawking emission of a $(1+1)$-dimensional acoustic black hole in a Bose-Einstein condensate. We use the brick wall model proposed by 't Hooft, adapted to the momentum space, in order to tackle the case when high frequency dispersion is taken in account. As expected, we find that in the hydrodynamic limit the entropy only depends on the size of the box in the near-horizon region, as for gravitational $(1+1)$-dimensional black holes. When dispersion effects are considered, we find a correction that depends on the square of the size of the near-horizon region measured in units of healing length, very similar to the universal correction to the entropy found in the case of spin-1/2 Heisenberg XX chains.

Few more comments added. Version accepted for publication in Physical Review D

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• Laval nozzle as an acoustic analogue of a massive field
• Hawking radiation and stability of the canonical acoustic black holes
• Thermodynamics of acoustic black holes in two dimensions
• Stochastic motion in an expanding noncommutative fluid
• Modified metrics of acoustic black holes: A review
• Analog dual to a 2+1-dimensional holographic superconductor
• A note on analogue semi-classical gravity in (1+1) dimensions
• Unusual Corrections to the Scaling of the Entanglement Entropy of the Excited states in Conformal Field Theory
• Effects of the Quantum Potential on lower dimensional models of analogue gravity
• Planar Black holes and Entanglement Entropy in Analog Gravity Models