Acoustic black holes, white holes, and wormholes in Bose-Einstein condensates in two dimensions

TL;DR

This paper explores stationary solutions of Bose-Einstein condensates in two dimensions that mimic black holes, white holes, and wormholes through spatially varying couplings, analyzing their properties, fluctuations, and Hawking radiation.

Contribution

It introduces a method to find stationary 2D BEC solutions with position-dependent couplings that simulate acoustic black/white holes and wormholes, including their thermal properties.

Findings

Existence of stationary 2D BEC solutions with supersonic regions

Derivation of approximate acoustic metric tensors for these solutions

Identification of conditions for Hawking temperature in specific potentials

Abstract

In a previous article, we studied stationary solutions to the dynamics of a Bose-Einstein condensate (BEC) corresponding to acoustic (or Unruh) black/white holes, namely configurations where the flow becomes supersonic creating a horizon for phonons. In this paper, we consider again the Gross-Pitaevskii Equation (GPE) but looking for stationary numerical solutions in the case where the couplings are position dependent in a prescribed manner. Initially we consider a 2D quantum gas in a funnel-like spatial metric. We then reinterpret this solution as a solution in a flat metric but with spatially dependent coupling and external potential. In these solutions the local speed of sound and magnitude of flow velocity cross, indicating the existence of a supersonic region and therefore of sonic analogues of black/white holes and wormholes. We discuss the numerical techniques used. We also study phase (and density) fluctuations in these solutions and derive approximate acoustic metric tensors. For certain external potentials, we find uniform density acoustic black hole configurations and obtain their Hawking temperature.