Acoustic metamaterial models on the (2+1)D Schwarzschild plane

[EN] Recent developments in acoustic metamaterial engineering have led to the design and fabrication of devices with formidable properties, such as acoustic cloaking, superlenses and ultra-sound waves. Artificial materials of this type are generally absent in natural environments. In this work, we focus on feasible implementations of acoustic black holes on the 2D plane, that is, within (2+1)D spacetime. For an accurate description of planar black holes in transformation acoustics, we examine Schwarzschild-type models. After proposing an appropriate form for the Lorentzian metric of the underlying spacetime, we explore the geometric content and physical consequences of such models, which will turn out to have de Sitter and anti-de Sitter spacetime structure. For this purpose, we derive a general expression for its acoustic wave propagation. Next, a numerical simulation is carried out for prototype waves which probe these spacetime geometries. Finally, we discuss how to fine-tune the corresponding acoustic parameters for an implementation in the laboratory environment.M. M. T. acknowledges financial support by the Spanish Ministerio de Economia y Competitividad, the European Regional Development Fund under grant TIN2014-59294-P, and the Generalitat Valenciana (BEST2017). He also wishes to thank for the cordial reception and hospitality at the Institute for Analysis and Scientific Computing of the Vienna University of Technology where part of the present work was established.Tung, MM.; Weinmüller, EB. (2019). Acoustic metamaterial models on the (2+1)D Schwarzschild plane. Journal of Computational and Applied Mathematics. 346:162-170. https://doi.org/10.1016/j.cam.2018.07.009S16217034

Metamaterial acoustics on the (2+ 1)D Einstein cylinder

[EN] The Einstein cylinder is the first cosmological model for our universe in modern history. Its geometry not only describes a static universe-a universe being invariant under time reversal-but it is also the prototype for a maximally symmetric spacetime with constant positive curvature. As such, it is still of crucial importance in numerous areas of physics and engineering, offering a fruitful playground for simulations and new theories. Here, we focus on the implementation and simulation of acoustic wave propagation on the Einstein cylinder. Engineering such an extraordinary device is the territory of metamaterial science, and we will propose an appropriate tuning of the relevant acoustic parameters in such a way as to mimic the geometric properties of this spacetime in acoustic space. Moreover, for probing such a space, we derive the corresponding wave equation from a variational principle for the underlying curved spacetime manifold and examine some of its solutions. In particular, fully analytical results are obtained for concentric wave propagation. We present predictions for this case and thereby investigate the most significant features of this spacetime. Finally, we produce simulation results for a more sophisticated test model which can only be tackled numerically.This work has been supported by the Spanish Ministerio de Economia y Competitividad, the European Regional Development Fund (ERDF) under grant TIN2017-89314-P, and the Programa de Apoyo a la Investigacion y Desarrollo 2018 (PAID-06-18) of the Universitat Politecnica de Valencia under grant SP20180016.Tung, MM. (2021). Metamaterial acoustics on the (2+ 1)D Einstein cylinder. Mathematics. 9(17):1-11. https://doi.org/10.3390/math9172079S11191