Perturbations of Schwarzschild black holes in laboratories

It is well known that the perturbations of Schwarzschild black holes are governed by a wave equation with some effective potential. We consider perturbations of a gas in a tube called the de Laval nozzle, which is narrow in the middle and has a sonic point in the throat. By equating the wave equation in a de Laval nozzle of an arbitrary form with the wave equation of spin-s perturbations of Schwarzschild black holes, we find the exact expression for the form of the de Laval nozzle, for which acoustic perturbations of the gas flow correspond to the general form of perturbations of Schwarzschild black holes. This allows observation, in a laboratory, of the acoustic waves, which are analog of damping quasinormal oscillations of Schwarzschild black holes. The found exact acoustic analog allows us to also observe some other phenomena governed by the wave equation, such as the wave scattering and tunneling