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

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.