Dissipative processes at the acoustic horizon

Abstract

A transonic fluid flow generates an acoustic hole that is the hydrodynamic analogue of a gravitational black hole. Acoustic holes emit a detectable thermal radiation of phonons at a characteristic Hawking temperature. The crucial concept is that the spontaneous phonon emission at the horizon produces an irreversible heat increase at the expenses of the bulk fluid kinetic energy. We show that such process can be described in terms of \textit{effective} shear and bulk viscosities that are defined close to the horizon. We analyze this quantum friction process by resorting to a general kinetic theory approach as well as by the specific description of phonon emission as a tunneling process. The celebrated Kovtun, Son and Starinets (KSS) universal lower bound $\eta /s = 1 / 4 \pi $ of the shear viscosity coefficient to entropy density ratio, readily follows, and is extended to the longitudinal bulk viscosity at the horizon. We come to the same saturation of the KSS bound after considering the shear viscosity arising from a perturbation of the background metric at the acoustic horizon providing a -- in principle testable -- realization of the so called black hole \textit{membrane paradigm}.