Unexpectedly large surface gravities for acoustic horizons?

Abstract

Acoustic black holes are fluid-dynamic analogues of generalrelativistic black holes, wherein the behaviour of soundwaves in a moving fluid acts as an analogue for scalar fieldspropagating in a gravitational background. Acoustichorizons, which are intimately related to regions where thespeed of the fluid flow exceeds the local speed of sound,possess many of the properties more normally associated withthe event horizons of general relativity, up to andincluding Hawking radiation. Acoustic black holes havereceived much attention because it would seem to be mucheasier to create an acoustic horizon experimentally than tocreate an event horizon. Here we wish to point outsome potential difficulties (and opportunities) in actuallysetting up an experiment that possesses an acoustic horizon.We show that in zero-viscosity, stationary fluid flow withgeneric boundary conditions, the creation of an acoustichorizon is accompanied by a formally infinite `surfacegravity', and a formally infinite Hawking flux. Only byapplying a suitable non-constant external body force, andfor very specific boundary conditions on the flow, can thesequantities be kept finite. This problem is ameliorated inmore realistic models of the fluid. For instance, addingviscosity always makes the Hawking flux finite (andtypically large), but doing so greatly complicates thebehaviour of the acoustic radiation - viscosity istantamount to explicitly breaking `acoustic Lorentzinvariance'. Thus, this issue represents both a difficultyand an opportunity - acoustic horizons may be somewhatmore difficult to form than naively envisaged, but ifformed, they may be much easier to detect than one would atfirst suppose.