摘要：在稀薄气体Bose-Einstein凝聚物中，存在动态稳定和不稳定的构型，其在流体动力学极限中表现出类似于重力黑洞的行为。动态不稳定性涉及在正和负能态中产生准粒子对，如在用于黑洞蒸发的公知的建议机制中。我们提出一种在环形陷阱中产生稳定的声波黑洞的方案。

对稀薄气体Bose-Einstein冷凝物的许多研究旨在实验地产生半经典平均场的非平凡配置，或预测在存在量子波动时这种配置的性质。这些问题对于凝聚体几乎不是特殊的，但是超稀释的稀薄气体是这样易于操作和控制，从实验上[1]和理论上[2]，他们可能允许我们通过类比分析不太适合的系统。作为这种冷凝物应用的一篇文章，在本文中，我们讨论了理论框架，并提出了一个实验，在实验室中创建一个黑洞的模拟，并模拟其辐射不稳定性。

事件视界[3]的流体动力学模拟最初由Unruh[4]提出作为一个更容易接近的现象，可能对霍金效应[5]（来自黑洞的热辐射，反向反应可忽略不计）特别是超高频的作用[6-8]。对于声波的事件范围原则上出现在任何具有闭合表面的地方，流体通过该闭合表面以声速向内流动，该流在表面的一侧上是亚音速的，在另一侧上是超音速的。在背景流体动力学流动上的声音传播与在弯曲时空中的场传播之间存在着近似的类比;虽然流体动力学只是物理（超）流体的长波长有效理论，因此弯曲空间中的场理论也被认为是量子重力的长波长近似[7,9]。在超液动力近似的完全计算中或在实际实验中确定声波黑洞是否以及如何发出声音，因此可以提供关于黑洞辐射及其对高频物理的灵敏度的一些建议。

我们的建议的基本挑战是保持被困的Bose-Einstein气体足够冷和良好隔离，以保持足够长的局部超音速流以观察其内在动力学。检测从地层辐射的热声子显然是一个困难的附加问题，因为这种辐射与许多其它可能的加热效应不可区分。然而，在我们的建议中不出现这种进一步的困难，因为我们预测的黑洞辐射，不像霍金辐射，不是准静态，而是在适当的条件下成指数增长。因此，在下一代原子陷阱中应该是可观察到的。

关键词：玻色-爱因斯坦凝聚（BEC）；Gross-Pitaevskii方程；Bose-Einstein气体

Summary：In the dilute gasous Bose-Einstein aggregates there is a dynamically stable and unstable configuration that exhibits behavior similar to gravity black holes in the hydrodynamic limit. Dynamic instability involves the generation of quasi-particle pairs in positive and negative energy states, as in well-known suggested mechanisms for black hole evaporation. We propose a scheme to produce a stable acoustic black hole in a circular trap.

Many studies of the Bose-Einstein condensate of the dilute gas are intended to experimentally produce nonspecific mean field non-trivial configurations or to predict the nature of such a configuration in the presence of quantum fluctuations. These problems are almost not special for condensates, but ultra dilution of dilute gas is so easy to manipulate and control, from experimental [1] and theoretical [2] aspect, they may allow us to analyze the systems that are less suitable by analogy. As an article in this condensate application, in this work we discuss the theoretical framework and propose an experiment to create a black hole in the lab to simulate and simulate its radiation instability.

The hydrodynamic simulations of the event horizon [3] were originally  proposed by Unruh [4] as a more accessible phenomenon that may be related to the Hawking effect [5] (heat radiation from the black hole, negatively reactive negatively) The role of frequency [6-8]. The event range for acoustic waves is, in principle, present at any place with a closed surface where the fluid flows inwardly through the closed  surface at a velocity of sound, which is subsonic on one side of the surface and supersonic on the other side. There is a similar analogy between the sound propagation on the background hydrodynamic flow and the field propagation in the curved space-time; although the hydrodynamics is only the long-wavelength theory of the physical (super) fluid, the field theory in the bending space is considered to be a long wavelength approximation of quantum gravity [7,9]. It is advisable to provide information about the black hole radiation and its sensitivity to high frequency physics in a complete calculation that exceeds the hydrodynamic approximation or in the actual  experiment to determine whether or not the acoustic black hole emits sound.