Unexpectedly large surface gravities for acoustic horizons?

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Abstract
Acoustic black holes are fluid-dynamic analogues of general relativistic black holes, wherein the behaviour of sound waves in a moving fluid acts as an analogue for scalar fields propagating in a gravitational background. Acoustic horizons, which are intimately related to regions where the speed of the fluid flow exceeds the local speed of sound, possess many of the properties more normally associated with the event horizons of general relativity, up to and including Hawking radiation. Acoustic black holes have received much attention because it would seem to be much easier to create an acoustic horizon experimentally than to create an event horizon. Here we wish to point out some potential difficulties (and opportunities) in actually setting up an experiment that possesses an acoustic horizon. We show that in zero-viscosity, stationary fluid flow with generic boundary conditions, the creation of an acoustic horizon is accompanied by a formally infinite `surface gravity', and a formally infinite Hawking flux. Only by applying a suitable non-constant external body force, and for very specific boundary conditions on the flow, can these quantities be kept finite. This problem is ameliorated in more realistic models of the fluid. For instance, adding viscosity always makes the Hawking flux finite (and typically large), but doing so greatly complicates the behaviour of the acoustic radiation - viscosity is tantamount to explicitly breaking `acoustic Lorentz invariance'. Thus, this issue represents both a difficulty and an opportunity - acoustic horizons may be somewhat more difficult to form than naively envisaged, but if formed, they may be much easier to detect than one would at first suppose.