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

TL;DR

This paper calculates the entanglement entropy of an acoustic black hole in a Bose-Einstein condensate, revealing how dispersion effects introduce universal corrections similar to those in quantum spin chains.

Contribution

It adapts the brick wall model to momentum space for Bose-Einstein condensate black holes, incorporating high-frequency dispersion effects into entropy calculations.

Findings

Entropy depends on the near-horizon region size in the hydrodynamic limit.

Dispersion introduces a correction proportional to the square of the near-horizon size in healing length units.

Correction resembles universal entropy correction in spin-1/2 Heisenberg XX chains.

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.