Acoustic Black Holes and Universal Aspects of Area Products

Abstract

In this paper we derive acoustic metrics in the (3+1)-dimensional Abelian Higgs model with higher derivative terms. We have found acoustic metrics that are conformally related to the Reissner-Nordstr\"om and Kerr-Newman metrics. The universal aspects of area products which depend only on quantized quantities such as conserved electric charge and angular momentum are also addressed. We relate these areas with entanglement entropy of acoustic black holes in BEC systems. We also have shown there is an equivalence between microscopic descriptions of axisymmetric acoustic black hole entropy in a BEC system in four and two dimensions. Particularly, the system seems to develop an analogue of the Kerr/CFT correspondence.