Metafluid models for higher-dimensional sonic black holes

This paper introduces and analyzes metafluid models for the design of two- and three-dimensional sonic black holes (SBHs), extending the concept of one-dimensional SBHs to higher dimensions. We propose a two-dimensional SBH (2D-SBH) consisting of geometrically radially graded domes embedded in a waveguide, which can be modeled as a metafluid with spatially varying density and sound speed. The governing wave equation for the 2D-SBH is derived and solved using both Gaussian expansion (GEM) and finite element (FEM) methods, demonstrating strong wave concentration effects at the SBH center. Ray tracing analysis further confirms the trapping behavior of the 2D-SBH and investigates the influence of key parameters such as residual thickness and SBH order. Additionally, we explore the potential of the 2D-SBH for noise reduction in rigid 2D cavities, showing significant attenuation above the SBH cut-on frequency. Finally, we extend the metafluid analogy to three dimensions (3D-SBH), using ray tracing to illustrate its wave-focusing capabilities. The simulation results suggest that higher-dimensional SBHs could serve as efficient acoustic absorbers and wave concentrators in practical applications.