Dissipative processes at the acoustic horizon

TL;DR

This paper explores the analogy between transonic fluid flows and black holes, showing that acoustic horizons exhibit dissipative processes characterized by effective viscosities, and confirms the universality of the KSS viscosity bound in this context.

Contribution

It introduces a kinetic theory framework to describe dissipative processes at acoustic horizons and extends the KSS viscosity bound to bulk viscosity in this analogue gravity system.

Findings

Effective shear and bulk viscosities are defined near the acoustic horizon.

The KSS bound $rac{ ext{eta}}{s} o rac{1}{4 ext{pi}}$ is confirmed for these viscosities.

Acoustic horizons provide a testable realization of the black hole membrane paradigm.

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}.