Historically, the Poincaré disk model has taken a pioneering role in the development of non-Euclidean geometry. But still today, this model is critical as a playground for simulations and new theories. In this paper, we discuss how to implement and simulate acoustic wave phenomena on the Poincaré disk with the help of so-called metamaterials. After formally developing a theory based on the acoustic potential for the curved spacetime of the Poincaré model, we also provide practical instructions on how to manufacture the appropriate metadevice in a laboratory environment. Finally, as an example, analytical results for the nontrivial radial contributions in concentric wave propagation are derived, and the corresponding numerical predictions are presented.

中文翻译：

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庞加莱圆盘上的超材料声学

从历史上看，庞加莱圆盘模型在非欧几何的发展中起到了开创性的作用。但直到今天，这个模型仍然是模拟和新理论的重要场所。在本文中，我们讨论了如何借助所谓的超材料在庞加莱圆盘上实现和模拟声波现象。在正式开发了基于 Poincaré 模型弯曲时空声势的理论之后，我们还提供了有关如何在实验室环境中制造合适的元设备的实用说明。最后，作为一个例子，导出了同心波传播中非平凡径向贡献的解析结果，并给出了相应的数值预测。