Phonon emission by acoustic black holes

We present a novel interpretation of the Hawking temperature of acoustic holes, the hydrodynamic analogue of standard black holes, by connecting the geometrical properties of the horizon with the distribution function of the spontaneously generated phonons. Using covariant kinetic theory to describe the phonon gas emitted by the acoustic hole, we obtain the correct expression of the Hawking temperature by equating the entropy loss of the acoustic horizon with the entropy gain of the phonon gas. In doing this, we assume that the entropy of the acoustic hole is proportional to the area of the horizon, as in standard black holes. Since our method only depends on the geometrical properties of the acoustic horizon and on the statistical properties of the phonon gas, it is well suited to be extended to standard black holes and to out-of-equilibrium systems.