  It is a deceptively simple question to ask how acoustic disturbances
propagate in a non-homogeneous flowing fluid. This question can be answered by
invoking the language of Lorentzian differential geometry: If the fluid is
barotropic and inviscid, and the flow is irrotational (though possibly time
dependent), then the equation of motion for the velocity potential describing a
sound wave is identical to that for a minimally coupled massless scalar field
propagating in a (3+1)-dimensional Lorentzian geometry. The acoustic metric
governing the propagation of sound depends algebraically on the density, flow
velocity, and local speed of sound. This rather simple physical system is the
basis underlying a deep and fruitful analogy between the black holes of
Einstein gravity and supersonic fluid flows. Many results and definitions can
be carried over directly from one system to another. For example, I will show
how to define the ergosphere, trapped regions, acoustic apparent horizon, and
acoustic event horizon for a supersonic fluid flow, and will exhibit the close
relationship between the acoustic metric for the fluid flow surrounding a point
sink and the Painleve-Gullstrand form of the Schwarzschild metric for a black
hole. This analysis can be used either to provide a concrete non-relativistic
model for black hole physics, up to and including Hawking radiation, or to
provide a framework for attacking acoustics problems with the full power of
Lorentzian differential geometry.
