A Covariant Spacetime Approach to Transformation Acoustics

Transformation acoustics focuses on the design of advanced acoustic devices by employing sophisticated mathematical transformation techniques for engineering acoustic metamaterials—materials artificially fabricated with extraordinary acoustic properties beyond those encountered in nature. We present differential-geometric methods together with a variational principle and show how they form the basis for a powerful framework to control acoustic waves in industrial applications. We conclude with a practical example and implement the acoustic wave equation within a uniform accelerating rigid frame (UAF). As expected, an acoustic event horizon emerges, i.e., a boundary in spacetime beyond which events cannot acoustically affect any outside observer.