Phonon motion around (2+1)-dimensional acoustic black hole

We study motion of a phonon, a particle representing the quanta of the sound wave in the (2+1) spacetime of the acoustic analogous axially symmetric black hole, so-called acoustic (sonic) black hole. Similar to the real objects known as black holes in relativity theories, the phenomenon called acoustic black hole possesses the ergoregion whose area is increasing with increasing rotation of the black hole, leading to more phonons being affected by the supersonic flow. It is found that phonons in the ergoregion of an acoustic black hole behave differently than those outside of it. Specifically, we found that the phonons in the ergoregion are affected by the supersonic flow of the fluid, causing them to move in different directions than those outside the ergoregion. Moreover, we presented calculations of the deflection angle and time delay of the phonon in the field of the acoustic black hole in the weak field regime that can be useful to test the geometry of the acoustic black hole in the laboratory.