Unexpectedly large surface gravities for acoustic horizons?

TL;DR

This paper investigates the theoretical challenges of creating acoustic horizons in fluid flows, revealing that infinite surface gravities occur under ideal conditions, but realistic factors like viscosity can make detection easier despite complicating the physics.

Contribution

It highlights the potential for infinite surface gravities in idealized acoustic horizons and explores how realistic effects like viscosity influence their formation and detectability.

Findings

Infinite surface gravity in ideal stationary flows with generic boundary conditions.

Viscosity renders Hawking flux finite but complicates acoustic radiation behavior.

Specific boundary conditions and external forces are required to keep physical quantities finite.

Abstract

Acoustic black holes are fluid dynamic analogs of general relativistic black holes, wherein the behaviour of sound waves in a moving fluid acts as an analog for scalar fields propagating in a gravitational background. Acoustic horizons possess many of the properties more normally associated with the event horizons of general relativity, up to and including Hawking radiation. They have received much attention because it would seem to be much easier to experimentally create an acoustic horizon than to create an event horizon. 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, but 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.