The entropy of an acoustic black hole in Bose-Einstein condensates: transverse modes as a cure for divergences

Understand

We consider the entropy associated to the phonons generated via the Hawking mechanism in a sonic hole in a Bose-Einsten condensate.

• In a previous paper, we looked at the (1+1)-dimensional case both in the hydrodynamic limit and in the case when high-frequency dispersion is taken in account.
• Here, we extend the analysis, based on the 't Hooft brick wall model, by including transverse excitations.
• We show that they can cure the infrared divergence that appears in the (1+1)-dimensional case, by acting as an effective mass for the phonons.