### 2.1 Background

The basic physics is this: A moving fluid will drag sound waves along with it, and if the speed of the fluid
ever becomes supersonic, then in the supersonic region sound waves will never be able to fight their way back
upstream [607, 622, 626, 624]. This implies the existence of a “dumb hole”, a region from which sound can not
escape.
Of course this sounds very similar, at the level of a non-mathematical verbal analogy, to the notion of a
“black hole” in general relativity. The real question is whether this verbal analogy can be turned into a
precise mathematical and physical statement – it is only after we have a precise mathematical and physical
connection between (in this example) the physics of acoustics in a fluid flow and at least some significant
features of general relativity that we can claim to have an “analogue model of (some aspects of)
gravity”.
Now the features of general relativity that one typically captures in an “analogue model” are the
kinematic features that have to do with how fields (classical or quantum) are defined on curved spacetime,
and the sine qua non of any analogue model is the existence of some “effective metric” that captures the
notion of the curved spacetimes that arise in general relativity. (At the very least, one might wish to capture
the notion of the Minkowski geometry of special relativity.) Indeed, the verbal description above (and its
generalizations in other physical frameworks) can be converted into a precise mathematical and physical
statement, which ultimately is the reason that analogue models are of physical interest. The analogy works
at two levels:

- Geometrical acoustics.
- Physical acoustics.

The advantage of geometrical acoustics is that the derivation of the precise mathematical form of the analogy is
so simple as to be almost trivial, and that the derivation is extremely general. The disadvantage is that in
the geometrical acoustics limit one can deduce only the causal structure of the spacetime, and does not
obtain a unique effective metric. The advantage of physical acoustics is that, while the derivation of the
analogy holds in a more restricted regime, the analogy can do more for you in that it can now
uniquely determine a specific effective metric and accommodate a wave equation for the sound
waves.