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 to be least neglected in Geometry. – Johannes Kepler

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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.
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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.

Analogies have played a very important role in physics and mathematics – they provide new ways of looking at problems that permit cross-fertilization of ideas among different branches of science. A carefully chosen analogy can be extremely useful in focusing attention on a specific problem, and in suggesting unexpected routes to a possible solution. In this review article we will focus on “analogue gravity”, the development of analogies (typically but not always based on condensed matter physics) to probe aspects of the physics of curved spacetime – and in particular to probe aspects of curved space quantum field theory, and to obtain lessons of potential relevance on the road towards a theory of quantum gravity.

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 example 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.

 1.1 Overview
 1.2 Motivations
 1.3 Going further

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