## Analogue Models

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# Analogue Models

## Background

Because experiments in Classical General Relativity are so difficult, many researchers are now becoming interested in the possibility of simulating aspects of general relativity using condensed matter analogues of curved spacetime. The basic idea is to look at the manner in which linearized perturbations propagate in some complicated condensed matter system, and then check whether in the particular system under consideration the characteristic surfaces describing the propagation fronts can be encoded in some sort of effective metric.

The simplest system to consider is that of sound in a moving fluid. If sound waves move with speed c in direction n relative to the fluid, and the fluid moves at velocity v relative to the laboratory, then relative to the laboratory the velocity of sound is

dx/dt = v + c n.

This is equivalent to saying that

dx = v dt + c n dt,

so that the sound cones are given by

(dx - v dt)² = c² n² dt²,

an observation which can be used to define an effective spacetime metric by

ds² = - c² n² dt² + (dx - v dt)².

Of course this metric needs not satisfy the Einstein equations, so you are not going to obtain all of the features of full general relativity, but you will have a good model for curved spacetime. More specifically those features of general relativity that are independent of the specific choice of field equations for the metric will be successfully mapped into our analogue model.

There is a long pre-history to analogue models, and many considerably more general condensed matter systems (and even more complicated systems) have been investigated. The modern revival of these ideas can be traced back to Bill Unruh's paper of 1980, though the field then remained largely inactive till the early 1990's. Over the last decade (1995-2005) roughly 150 scientific papers have been written addressing one or another feature of analogue models.

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## Analogue models at Victoria University of Wellington

Matt Visser has been involved in the analogue gravity programme since 1993, and has now been author or co-author on approximately 20 papers on this subject. This topic continues to be a major focus of the activities of the Victoria University Gravity Group with specific interests in:

• Analogue black holes, and specifically real-world examples of analogue black holes.
• Hawking radiation and more generally black hole thermodynamics from analogue black holes.
• The use of Bose Einstein condensates (BECs) as a working fluid for the analogue models.
• Causal structure in analogue models.
• The use of analogue models as specific toy models of Lorentz symmetry breaking.
• Multiple metric structures in analogue models; birefringence, bimetricity, and Fresnel equations.

A brief bibliography of analogue models can be found here.

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