Particle scattering in a sonic analogue of special relativity

We investigate a simple toy model of particle scattering in the flat spacetime limit of an analogue-gravity model. The analogue-gravity medium is treated as a scalar field of phonons that obeys the Klein--Gordon equation and thus admits a Lorentz symmetry with respect to {c}_{\mathrm{s}} the speed of sound in the medium. The particle from which the phonons are scattered is external to the system and does not obey the sonic Lorentz symmetry...