Bibliography: Analog models of General Relativity

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This document is an attempt at a reasonably complete bibliography on analog methods.

Comments and suggestions should be sent to Matt Visser:

Remember that analog methods can be used for at least three distinct purposes:

Because "analog models" means such different things to different authors, and because many of the authors below worked in isolation from the others, you may detect a certain lack of coherent viewpoint in the papers cited below.
(In particular, the work initiated in the 1990's using analog models to probe the concept of Hawking radiation was developed largely in ignorance of what had been done before.)


Warning: This bibliography is still rather fragmentary. It will be extended and improved as time permits.

Historical period (Optics):

Perhaps the first paper to seriously discuss analog models and effective metric techniques was that of Walther Gordon (yes, he of the Klein-Gordon equation): Note that Gordon seemed largely interested in trying to describe dielectric media by an "effective metric". That is: Gordon wanted to use a gravitational field to mimic a dielectric medium.

After that, there was sporadic interest in effective metric techniques. One historically important contribution was one of the *problems* in Landau and Lifshitz:

Note that in contrast to Gordon, here the interest is in using dielectric media to mimic a gravitational field.

In France the idea was taken up by Pham Mau Quan:

Three articles that directly used the dielectric analogy to analyze specific physics problems are:

The general formalism was more fully developed in articles such as: A good summary of this classical period is due to Fernando de Felice: In summary and with hindsight:

Historical period (Acoustics):

There were several papers in the 1970's and 1980's using an acoustic analogy to investigate the propagation of shockwaves in astrophysical situations:

Recent period (Acoustics):

General Relativists re-focussed interest in this topic after the key paper of Unruh: After a delay of another decade, Unruh's article lead to an explosion of interest, with particular relevance to the Hawking radiation process:

Recent period (Superfluids --- Liquid Helium):

The use of superfluid systems, in particular liquid Helium, has been extensively discussed by Volovik and co-workers:

Recent period (Optical systems):

The use of "slow light" seems a promising system for experimental implementation.
These are systems in which (over a limited range of frequencies) the group-refractive-index is extremely high and the group velocity extremely low
(though the phase-refractive-index is unity and the phase velocity is the usual speed of light).
Current [Y2K] experimental limits on the group velocity of light are at the level of 50 centimetres/second.

Recent period (Bose-Einstein condensates):

The acoustic properties of Bose-Einstein condensates are also of great experimental interest. Sound velocities (propagation speeds for perturbations in the phase of the condensate wavefunction) can be as low as millimetres/second.

Recent period (Nonlinear electrodynamics):

Quantum corrections in QED lead to non-linear electrodynamics: electrodynamics that is not described by the usual Maxwell Lagrangian but by the more general Schwinger Lagrangian (containing F^4 terms and higher).

To lowest order in the fine structure, the Schwinger Lagrangian reduces to the Euler-Heisenberg Lagrangian.

Alternatively, by appealing to string theory, one can justify interest in the Born-Infeld Lagrangian.

All these examples of nonlinear electrodynamics lead to situations where the propagation of photons can be described by looking at the geodesics of an "effective metric" that is an algebraic function of the background electromagnetic field. See:

Recent period (Unclassified section):

A lot of relevant papers have appeared in the last 10 years or so (1991-2000).
Sometimes it is a little difficult to classify them.
To be included below the paper must at least have something to say about "effective metric" techniques.
That is, there should be some notion of an "effective metric", physically distinct from the spacetime metric of general relativity, that nevertheless influences the propagation of waves, signals, or particles in some manner.

The references below still need to be ordered and categorized:

I do not claim to have an exhaustive bibliography.

Additional suggestions are welcome.

Extensive construction still in progress!

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Last updated 28 November 2000
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