1 Introduction

And I cherish more than anything else the Analogies, my most trustworthy masters. They know all the secrets of Nature, and they ought least to be neglected in Geometry. -- Johannes Kepler

Figure 1:

Artistic impression of cascading sound cones (in the geometrical acoustics limit) forming an acoustic black hole when supersonic flow tips the sound cones past the vertical.

Figure 2:

Artistic impression of trapped waves (in the physical acoustics limit) forming an acoustic black hole when supersonic flow forces the waves to move downstream.

The most well-known of these analogies is the use of sound waves in a moving fluid as an analogue for light waves in a curved spacetime. Supersonic fluid flow can then generate a “dumb hole”, the acoustic analogue of a “black hole”, and the analogy can be extended all the way to mathematically demonstrating the presence of phononic Hawking radiation from the acoustic horizon. This particular provides (at least in principle) a concrete laboratory model for curved-space quantum field theory in a realm that is technologically accessible to experiment.

There are many other “analogue models” that may be useful for this or other reasons - some of the analogue models are interesting for experimental reasons, others are useful for the way they provide new light on perplexing theoretical questions. The information flow is in principle bi-directional and sometimes insights developed within the context of general relativity can be used to understand aspects of the analogue model.

Of course analogy is not identity, and we are in no way claiming that the analogue models we consider are completely equivalent to general relativity - merely that the analogue model (in order to be interesting) should capture and accurately reflect a sufficient number of important features of general relativity (or sometimes special relativity). The list of analogue models is extensive, and in this review we will seek to do justice both to the key models, and to the key features of those models.

In the following chapters we shall:

Discuss the flowing fluid analogy in some detail.

Summarise the history and motivation for various analogue models.

Discuss the many physics issues various researchers have addressed.

Provide a (hopefully complete) catalogue of extant models.

Discuss the main physics results obtained to date.

Outline the many possible directions for future research.

Summarise the current state of affairs.

By that stage the interested reader will have had a quite thorough introduction to the ideas, techniques, and hopes of the analogue gravity programme.